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Summary: Identifying genomic regions involved in the differences between breeds can provide information on genes that are under the influence of both artificial and natural selection. The aim of this study was to assess the genetic diversity and differentiation among four different Brown cattle populations (two original vs. two modern populations) and to characterize the distribution of runs of homozygosity (ROH) islands using the Illumina Bovine SNP50 BeadChip genotyping data. After quality control, 34 735 SNPs and 106 animals were retained for the analyses. Larger heterogeneity was highlighted for the original populations. Patterns of genetic differentiation, multidimensional scaling, and the neighboring joining tree distinguished the modern from the original populations. The FST‐outlier identified several genes putatively involved in the genetic differentiation between the two groups, such as stature and growth, behavior, and adaptability to local environments. The ROH islands within both the original and the modern populations overlapped with QTL associated with relevant traits. In modern Brown (Brown Swiss and Italian Brown), ROH islands harbored candidate genes associated with milk production traits, in evident agreement with the artificial selection conducted to improve this trait in these populations. In original Brown (Original Braunvieh and Braunvieh), we identified candidate genes related with fat deposition, confirming that breeding strategies for the original Brown populations aimed to produce dual‐purpose animals. Our study highlighted the presence of several genomic regions that vary between Brown populations, in line with their different breeding histories. [ABSTRACT FROM AUTHOR]

Lactose percentage (LP) in milk is currently determined in most herd-testing schemes, and globally, it is usually routinely recorded in the framework of the official milk recording procedures. However, few studies have investigated the phenotypic and genetic variability of this component. Data used in the present paper consisted of 59 811 test-day records from 4355 Holstein cows in 266 herds. Heritabilities of LP and lactose yield (LY) were estimated through single-trait repeatability animal models, whereas genetic and phenotypic correlations of LP and LY with milk composition and production traits, somatic cell score and milk freezing point were estimated using bivariate models. Fixed effects included in the analyses were herd-test-date, season of calving, parity, stage of lactation and the interaction between parity and stage of lactation. Random effects were animal additive genetic, within and across lactation permanent environment and the residual. Lactation curves of LP and LY increased from parturition to the peak of lactation and decreased thereafter, mirroring the typical curve of milk yield. Lactose percentage was greater in first- than later-parity cows. Heritabilities of LP and LY were 0.43±0.03 and 0.14±0.02, respectively, and LP and protein percentage were the most repeatable traits. Genetic correlations (r a) of LP with somatic cell score, LY and milk freezing point were −0.22±0.08, 0.28±0.08 and −0.46±0.05, respectively. Genetic relationships of LY with milk yield (r a=0.97±0.00), fat percentage (r a=−0.71±0.06), protein percentage (r a=−0.57±0.06) and protein yield (r a=0.64±0.06) were moderate to strong. Results suggest that milk LP could be considered in breeding strategies to accelerate the gain of correlated low heritable traits. Further research is needed to evaluate the feasibility of including LP in the selection index of Italian Holstein population to address country-specific needs and market demands. [ABSTRACT FROM AUTHOR]

Milk mineral concentration is important from both the perspective of processing milk into dairy products and its nutritive value for human consumption. Precise estimates of genetic parameters for milk mineral concentration are lacking because of the considerable resources required to collect vast phenotypes quantities. The milk concentration of calcium (Ca), potassium (K), magnesium (Mg), sodium (Na) and phosphorus (P) in the present study was quantified from mid-IR spectroscopy on 12 223 test-day records from 1717 Holstein-Friesian cows. (Co)variance components were estimated using random regressions to model both the additive genetic and within-lactation permanent environmental variances of each trait. The coefficient of genetic variation averaged across days-in-milk (DIM) was 6.93%, 3.46%, 6.55%, 5.20% and 6.68% for Ca, K, Mg, Na and P concentration, respectively; heritability estimates varied across lactation from 0.31±0.05 (5 DIM) to 0.67±0.04 (181 DIM) for Ca, from 0.18±0.03 (60 DIM) to 0.24±0.05 (305 DIM) for K, from 0.08±0.03 (15 DIM) to 0.37±0.03 (223 DIM) for Mg, from 0.16±0.03 (30 DIM) to 0.37±0.04 (305 DIM) for Na and from 0.21±0.04 (12 DIM) to 0.57±0.04 (211 DIM) for P. Genetic correlations within the same trait across different DIM were almost unity between adjacent DIM but weakened as the time interval between pairwise compared DIM lengthened; genetic correlations were weaker than 0.80 only when comparing both peripheries of the lactation. The analysis of the geometry of the additive genetic covariance matrix revealed that almost 90% of the additive genetic variation was accounted by the intercept term of the covariance functions for each trait. Milk protein concentration and mineral concentration were, in general, positively genetically correlated with each other across DIM, whereas milk fat concentration was positively genetically correlated throughout the entire lactation with Ca, K and Mg; the genetic correlation with fat concentration changed from negative to positive with Na and P at 243 DIM and 50 DIM, respectively. Genetic correlations between somatic cell score and Na ranged from 0.38±0.21 (5 DIM) to 0.79±0.18 (305 DIM). Exploitable genetic variation existed for all milk minerals, although many national breeding objectives are probably contributing to an indirect positive response to selection in milk mineral concentration. [ABSTRACT FROM AUTHOR]

In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter $$\lambda .$$ We introduce a notion of sensitivity of the process to its initial condition and prove that it increases not only for values of $$\lambda < \lambda _c, $$ the value of the critical parameter, but keeps increasing even after $$ \lambda _c , $$ before finally starting to decrease for values of $$\lambda $$ sufficiently above $$\lambda _c.$$ This provides a counterexample to the common belief that associates maximal information transmission to criticality. [ABSTRACT FROM AUTHOR]

The article presents a case study involving comparison of genetic diversity of Turkish and Italian local chicken breeds for further conservation strategies.

We consider a highly anisotropic $$d=2$$ Ising spin model whose precise definition can be found at the beginning of Sect. 2. In this model the spins on a same horizontal line (layer) interact via a $$d=1$$ Kac potential while the vertical interaction is between nearest neighbors, both interactions being ferromagnetic. The temperature is set equal to 1 which is the mean field critical value, so that the mean field limit for the Kac potential alone does not have a spontaneous magnetization. We compute the phase diagram of the full system in the Lebowitz-Penrose limit showing that due to the vertical interaction it has a spontaneous magnetization. The result is not covered by the Lebowitz-Penrose theory because our Kac potential has support on regions of positive codimension. [ABSTRACT FROM AUTHOR]

The aim of the present study was to estimate genetic parameters for calcium (Ca), phosphorus (P) and titratable acidity (TA) in bovine milk predicted by mid-IR spectroscopy (MIRS). Data consisted of 2458 Italian Holstein−Friesian cows sampled once in 220 farms. Information per sample on protein and fat percentage, pH and somatic cell count, as well as test-day milk yield, was also available. (Co)variance components were estimated using univariate and bivariate animal linear mixed models. Fixed effects considered in the analyses were herd of sampling, parity, lactation stage and a two-way interaction between parity and lactation stage; an additive genetic and residual term were included in the models as random effects. Estimates of heritability for Ca, P and TA were 0.10, 0.12 and 0.26, respectively. Positive moderate to strong phenotypic correlations (0.33 to 0.82) existed between Ca, P and TA, whereas phenotypic weak to moderate correlations (0.00 to 0.45) existed between these traits with both milk quality and yield. Moderate to strong genetic correlations (0.28 to 0.92) existed between Ca, P and TA, and between these predicted traits with both fat and protein percentage (0.35 to 0.91). The existence of heritable genetic variation for Ca, P and TA, coupled with the potential to predict these components for routine cow milk testing, imply that genetic gain in these traits is indeed possible. [ABSTRACT FROM PUBLISHER]

Copyright of Animal Genetic Resources is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aim of this study was to estimate (co)variance components for milk coagulation properties (MCP) predicted by mid-infrared spectroscopy (MIRS) during routine milk recording, and to assess their relationships with yield and quality traits. A total of 63 470 milk samples from Holstein-Friesian cows were analyzed for MCP, pH and quality characteristics using MIRS. Casein to protein and protein to fat ratios were calculated from information obtained by MIRS. Records were collected across 1 year on 16 089 cows in 345 herds. The model used for genetic analysis included fixed effects of parity and stage of lactation, and random effects of herd-test-day, cow permanent environmental, animal additive genetic and residual. (Co)variance components were assessed in a Bayesian framework using the Gibbs Sampler. Estimates of heritabilities were consistent with those reported in the literature, being moderate for MCP (0.210 and 0.238 for rennet coagulation time (RCT) and curd firmness (a30), respectively), milk contents (0.213 to 0.333) and pH (0.262), and low for somatic cell score (0.093) and yield traits (0.098 to 0.130). Repeatabilities were 0.391 and 0.434 for RCT and a30, respectively, and genetic correlations were generally low, with estimates greater than 0.30 (in absolute value) only for a30 with fat, protein and casein contents. Overall, results suggest that genetic evaluation for MCP predicted by MIRS is feasible at population level, and several repeated measures per cow during a lactation are required to estimate reliable breeding values for coagulation traits. [ABSTRACT FROM PUBLISHER]

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase. [ABSTRACT FROM AUTHOR]

The aim of this study was to estimate genetic parameters for type traits of hypertrophic Piemontese cows. Seven traditional type trait evaluations (70 to 100 grid scores), 2 body measurements (cm), and 13 linear description traits (1 to 9 grid scores) recorded on 21,757 Piemontese primiparous cows reared in 990 farms were used. Data were analyzed using a multiple-trait (22 traits) animal model with canonical transformation, accounting for a unique design matrix with the following effects: herd-year-classifier, days in milk, age at calving, and the genetic additive cow effect. Heritability estimates of traditional type evaluation traits were low for thorax, rump, feet and legs, and dairyness (≤0.10), intermediate for fleshiness and overall score evaluations (0.13 to 0.15), and medium to high for body size (0.26). Genetic correlations of dairyness with all the other traditional type traits were low (from -0.14 to 0.16), those of feet and legs were moderate (0.19 to 0.44), and the remaining 5 traits were high (≥0.55), with an exception regarding fleshiness and body size (0.28). Medium-high heritability estimates were obtained for withers height (0.31) and trunk length (0.21), with a very high genetic correlation between these traits (0.97). The genetic correlations of body measurements with body size were also very high (about 0.96), high with thorax, rump, and overall score (0.47 to 0.59), and moderate with the other traditional type traits (0.04 to 0.27). Heritability estimates of all linear traits were moderate (0.09 to 0.15), with the exceptions of top line (0.07) and condition score (0.05). Genetic correlations between linear traits were generally low to moderate (from -0.11 to 0.44) with the only exceptions of the 6 fleshiness traits and body condition, which showed very high correlations (0.60 to 0.96). Moreover, skeletal traits as top line, bone thinness, and head scores presented moderate genetic correlations (0.51 to 0.65). Genetic correlations between linear traits and traditional type traits were consistent with the trend observed between type traits. In conclusion, body measurements seem to describe body size better than traditional evaluation or linear descriptors. The genetic correlations among type evaluation and linear description traits suggest the need for a reduction in the number of traits scored, particularly of those relating to muscular development. [ABSTRACT FROM AUTHOR]

1. An experiment involving 60 male chickens reared in an organic production system was carried out in order to investigate carcase characteristics and qualitative meat traits of three slow-growing Italian local breeds of chicken (Ermellinata, Padovana and Pepoi). 2. Chicks were randomly selected at hatch, raised together under the same conditions, slaughtered at 190 d of age, dissected for carcase traits, and meat (breast and thigh) stored for subsequent analysis of quality parameters. 3. Ermellinata (EA) chickens were significantly different from Padovana (PA) and Pepoi (PI) chickens for live, carcase and thigh weights. Breeds were also different for breast muscle protein content (EA > PI and PA), shear force (PA < EA and PI) and cooking loss (PI > PA and EA) values. 4. The CIE system values of lightness (L*), redness (a*), and yellowness (b*) evidenced a distinctive darker meat and lighter skin colour of PA breast meat. 5. Polyunsaturated fatty acids composition of breast meat was similar among the analysed breeds. EA had significantly higher saturated but significantly lower monounsaturated fatty acid contents than the other two breeds. [ABSTRACT FROM AUTHOR]

The aim of the study was to assess crossbreeding effects for 305-day milk, fat, and protein yield and calving interval (CI) in Irish dairy cows (parities 1 to 5) calving in the spring from 2002 to 2006. Data included 188 927 records for production traits and 157 117 records for CI. The proportion of genes from North American Holstein Friesian (HO), Friesian (FR), Jersey (JE) and Montbéliarde (MO) breeds, and coefficients of expected heterosis for HO×FR, HO×JE and HO×MO crosses were calculated from the breed composition of cows’ parents. The model used to assess crossbreeding effects accounted for contemporary group, age at calving within parity, linear regression on gene proportions for FR, JE and MO, and linear regression on coefficients of expected heterosis for HO×FR, HO×JE and HO×MO, as fixed effects, and additive genetic, permanent environmental and residual as random. Breed effects for production traits were in favour of HO, while for CI were in favour of breeds other than HO. The highest heterosis estimates for production were for HO×JE, with first-generation crosses yielding 477 kg more milk, 25.3 kg more fat, and 17.4 kg more protein than the average of the parental breeds. The highest estimate for CI was for HO×MO, with first-generation crosses showing 10.2 days less CI than the average of the parental breeds. Results from this study indicate breed differences and specific heterosis effects for milk yield traits and fertility exist in Irish dairy population. [ABSTRACT FROM AUTHOR]

We consider the Potts model in $$\mathbb R^d$$ , $$d\ge 2$$ , with $$q \ge 3$$ states and prove that for all values of the inverse temperature $$\beta $$ which are small enough there is a critical value $$z_c(\beta )$$ of the fugacity so that at $$(\beta ,z_c(\beta ))$$ there are $$q+1$$ extremal DLR measures (thus the phase transition is of first order). The first q have a spin which appears with higher frequency than the other spins while in the last one all the spins have the same frequency, moreover the particle density is strictly smaller than in the first q states. [ABSTRACT FROM AUTHOR]

The genetic variability and presence of population substructures in 4 native Northern Italian sheep breeds, Alpagota, Brogna, Foza, and Lamon, undergoing in situ conservation, and 1 widespread Italian breed, Bergamasca, were studied by investigating 19 microsatellite markers. The breeds showed considerable genetic variability in terms of number of alleles and heterozygosity, with the exception of Alpagota, which was the least variable (0.607). Nevertheless, a significant deficit of heterozygotes was observed in each breed due to rather increased levels of inbreeding or to the presence of population substructures, probably caused by increased genetic variation in the founder populations. The analyses evidenced clear genetic differentiation (FST = 0.085), reduced levels of admixture, and presence of private alleles among the breeds, confirm- ing their genetic uniqueness. In particular, according to Reynolds genetic distances, Alpagota was the most differentiated, perhaps because it had been bred mostly in a rather isolated area. Loss of any of the investigated breeds would result in a loss of genetic diversity ranging from 0.5 to 1.6% of the total observed gene diversity. Results supported the decision to safeguard these breeds as important reservoirs of genetic diversity and suggested breeding and mating practices to maintain variability and to overcome within-breed sub-structures. [ABSTRACT FROM AUTHOR]

In Italy more than fifty different local breeds of chicken ( Gallus gallus L.) are known to have been present in the past. The overall situation is now critical since most of these breeds are becoming extinct or threatened and only a few are subject of conservation plans. The use of molecular markers for the analysis of chicken populations could help in characterizing their genetic variation and preserving them from genetic erosion. valuable and irreplaceable sources of chicken germplasm from indigenous populations of the veneto region were analyzed by means of DNA fingerprinting with molecular markers designed on interspersed mini- and micros-atellite repeats. The identification of either among-breed discriminant or breed-specific markers was based on the S-SAP and M-AFLP systems derived from the AFLP technology. Genomic DNA fingerprints were generated in 84 individuals belonging to six local breeds (Ermellinata, Padovana, Pépoi, Polverara, Robusta Lionata and Robusta Maculata) and one commercial line used as reference standard. A number of variation statistics were computed to assess the genetic variability within and relatedness among breeds: the effective number of alleles per locus (ne= 1.570), total and single-breed genetic diversity (HT= 0.366 and HS= 0.209, respectively) and the fixation index (GST= 0.429). The mean genetic similarity coefficients within and between local breeds were 0.769 and 0.628, respectively. Markers useful for the genetic traceability of breeds revealed significant sequence similarities with either genic or intergenic regions of known chromosome position. Sequence tagged site primers were designed for the most discriminant markers in order to develop multiplex non-radioactive genomic PCR assays. Analysis of the population structure along with individual assignment tests successfully identified all breed clusters and subclusters. The vast majority of animals were correctly allocated to their breed of origin, demonstrating the suitability and reliability of the chosen AFLP-derived marker systems for detecting population structure and tracing individual breeds. The local breeds have been preliminarily identified according to sequence-specific SNPs and haplotypes and the polymorphism information content of genomic AFLP-derived markers is reported and critically discussed. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the effect of different breeds and breed crosses on age (AC, d), BW (kg), price (PR, $/kg), and market value (MV, $/calf) of purebred and crossbred calves sold for veal and beef production. The Kovieh wholesale cattle organization (Bolzano, Italy) grouped calves from several dairy herds located in the Trentino-Südtirol region in Italy and sold them by public auctions. Data on AC, BW, PR, and MV from 96,458 calves were recorded from January 2003 to December 2007 and consisted of 4 pure breeds [2 dairy, Brown Swiss (BS) and Holstein- Friesian (HF); and 2 dual-purpose, Simmental (SI) and Alpine Grey (AG)], and 8 crossbreds by crosses of Limousin (LI) and Belgian Blue (BB) with the 4 dam breeds. Least squares means for AC, BW, PR, and MV were calculated for breeds and breed crosses with a model that included fixed effects of herd of birth, age (except for AC), sex, and breed of the calf, year and season of auction, and interactions between the main effects. The coefficients of determination of the models were 0.41, 0.51, 0.84, and 0.82 for AC, BW, PR, and MV, respectively. Sex, age, and breed were the most relevant sources of variation for BW (P < 0.001), whereas breed and sex were the most important sources of variation for AC, PR, and MV (P < 0.001). Also, PR and MV were significantly influenced (P < 0.01) by all the effects included in the model, except for season x age interaction in the case of MV. Market value of male was greater (P < 0.001) than that of female calves, with the exception of BS (-$28.76/calf) and HF (-$20.70/calf) purebred males. Dual-purpose purebred calves presented greater (P < 0.001) PR and MV than dairy purebreds (MV of $426.97/calf and $307.96/ calf for SI and AG, and $256.24/calf and $275.65/calf for BS and HF, respectively). Calves from SI and AG dams had greater (P < 0.001) BW, PR, and MV than calves from BS and HF dams. Calves from SI cows had greater (P < 0.001) BW, PR, and MV than calves from AG cows. Crossbreeding with beef bulls increased (P < 0.001) BW, PR, and MV of calves from dairy and dual- purpose dams. Crossbreeding with BB bulls increased PR (+$2.58 ± 0.04/kg; P < 0.001) and MV (+$190.84 ± 3.62/calf; P < 0.001) of calves much more than LI. The use of beef bull semen on dairy herds resulted in an economic revenue from selling crossbred calves. [ABSTRACT FROM AUTHOR]

The present study was a contribution on the genetic characterization of the Burlina local cattle breed, and an approach to understanding the relationships between Burlina, Holstein Friesian and Brown Swiss which represent the majority of the dairy cattle reared nowadays in North-East Italy. The obtained results helped to clarify the genetic diversity and distinctiveness of Burlina population. In particular, the low genetic distance between Burlina and Holstein Friesian and the assignment of a moderate percentage of Burlina animals to Holstein Friesian suggested that crosses between them took place in the past, while crosses with Brown Swiss seemed to be less frequent. However, analyses of marker genotypes, showed a cluster with only Burlina individuals, which demonstrates the genetic distinctness of this breed. The Burlina breed showed the highest variability among the analysed breeds and its inbreeding coefficient was low. The data contribute to the feasibility of a conservation and selection programme for this breed and the results are useful for the implementation of a conservation strategy that should aim to conserve animals where the contribution from foreign breeds is as small as possible. [ABSTRACT FROM AUTHOR]

Genetic variation in four indigenous chicken breeds from the Veneto region of Italy was assessed using amplified fragment length polymorphism (AFLP) markers. A total of 99 individuals were analysed using three AFLP primer combinations that produced 70 polymorphisms. Four indigenous Veneto chicken breeds (Ermellinata, Padovana, Pépoi and Robusta) and a reference broiler line were included in the analysis. Breed-specific markers were identified in each breed. The expected heterozygosity did not differ significantly among the indigenous Veneto chicken breeds and the broiler line. The coefficient of gene variation (Gst) value across loci indicated that almost half of the total variability was observed among breeds. Nei's standard genetic distance between pairs of breeds showed that the distance between the broiler line and the Pépoi breed was greater than the distances between the broiler line and the other three chicken breeds. Cluster analysis based on standard genetic distances between breeds indicated that the Padovana and Pépoi breeds were closely related. Factorial analysis based on a binary matrix of the AFLP data showed a clear distinction of all breeds. [ABSTRACT FROM AUTHOR]

We consider one-dimensional spin systems with Hamiltonian:, where ɛ are independent random variables and, using decimation and the cluster expansion, we show that, when α>3/2 and E(ɛ)=0, for any magnetic field h and inverse temperature β, the correlation functions and the free energy are C both in h and β. Moreover we discuss an example, obtained by a particular choice of the probability distribution of the ɛ's, where the quenched magnetization is C but fails to be analytic in h for suitable h and β. [ABSTRACT FROM AUTHOR]

We consider one dimensional systems described by many body potentials with finite first moment and prove that the correlation functions are analytic in the interaction parameters. This result is not new (Dobrushin, 1973) but our proof is simpler and physically more transparent. We show that by introducing suitable blocks and averaging over the variables associated to a subset of the blocks (decimation procedure), the resulting effective interaction is such that the system can always be dealt with as a high temperature system. [ABSTRACT FROM AUTHOR]

We develop a technique for reducing the problem of the ultraviolet divergences and their removal to a free field problem. This work is an example of a problem to which a rather general method can be applied. It can be thought as an attempt towards a rigorous version (in 2 or 3 space-time dimensions) of the analysis of the structure of the functional integrals developed in [9], the underlying mechanism being essentially the same as in [11,3]. [ABSTRACT FROM AUTHOR]

We study, in the context of the Markov hyerarchical fields ( d=2, 3) the role of the Markov property, of formal renormalization and of formal positivity. We determine upper and lower bounds for the ground state energy and discuss their relation with the perturbation theory series. [ABSTRACT FROM AUTHOR]

A system of random variables(spins) S,x∈ℤ , taking on values in ℝ is considered. Conditional probabilities for the joint distributions of a finite number of spins are prescribed; a DLR measure is then a process on the random variables which is consistent with the assigned conditional probabilities [1,2]. A case of physical interest both in Statistical Mechanics and in the lattice approximation to Quantum Field Theory is considered for which the spins interact pairwise via a potential JSS, J∈ℝ and via a self-interaction F(S), which, as ¦ S¦→∞, diverges at least quadratically [3]. By use of a technique introduced in [2] it is proven that the set is a compact (in the local weak topology, Def. 1.1) non-void Choquet simplex [4]. Sufficient conditions are then given in order to obtain the measures in $$\mathfrak{E}$$ as limits of Gibbs measures for finitely many spins in a wide class of boundary conditions, Theorem 1.2. Uniqueness in $$\mathfrak{E}$$ is then discussed by means of a theorem by Dobrušin [2] and a sufficient condition for unicity is obtained which can be physically interpreted as a mean field condition [5]. Therefore the mean field temperature is rigorously proven to be an upper bound for the critical temperature. [ABSTRACT FROM AUTHOR]

We attempt to present in a systematic fashion a theory of critical behavior in terms of simple probabilistic concepts. This approach arose out of renormalization group treatments of critical phenomena in phase transitions, but it is relevant also for turbulence, certain geophysical situations, and in general for any statistical problem in which scaling laws are expected to play a significant role. The presentation here reflects the recent emphasis on phase transitions but the formulation is sufficiently general to be easily adapted for a different context. Familiarity with probability theory at an elementary level is the only prerequisite for following this article.
In this article we deal with some developments in the theory of critical phenomena which make contact with corresponding problems in the theory of stochastic processes and provide an interpretation in probabilistic terms of the renormalization group approach. In this way, the renormalization group idea acquires a deeper and wider significance than one is led to expect by the technicalities which usually hamper expositions of the subject. [ABSTRACT FROM AUTHOR]

We consider a lattice model with a repulsive hard core and an attractive short range interaction. We show that this model has at least three independent equilibrium states, when the temperature is sufficiently low and the chemical potential is suitably chosen. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional Ising ferromagnet with (+) boundary conditions and negative external field, where a Markovian time evolution is assumed. We construct, suitably restricting the allowed configurations at t=0, a non equilibrium state with positive magnetization such that: These results are obtained following a general method for describing metastable states proposed by Lebowitz and Penrose and exploiting the analysis of the Ising-spin-configurations in terms of contours given by Minlos and Sinai. [ABSTRACT FROM AUTHOR]

The original idea of Ruelle, to associate classes of configurations of the continuous Widom and Rowlinson model to contours on a lattice, is exploited to get for this model an expression of the grand partition function very similar to that of the Ising system. This allows to get, when the activities are high enough, a microscopic description of this system as a mere transcription of Minlos and Sinai analysis of the Ising model at low temperatures. [ABSTRACT FROM AUTHOR]

Copyright of Il Nuovo Cimento: B is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The one to one correspondence between the existence of a unique equilibrium state and the differentiability of the free energy density with respect to the external field previously shown for Ising ferromagnetis is extendend to higher valued spin systems as well as to continuum systems satisfying the Fortuin, Kasteleyn and Ginibre inequalities. In particular this is shown to hold for a mixture of A - B particles in which there is no interaction between like particles and a repulsion between unlike particles. Where the derivative of the free energy is discontinuous there are at least two equilibrium states. [ABSTRACT FROM AUTHOR]

We investigate low temperature properties of an Ising ferromagnet when the nearest neighbour coupling constant is dominant. We show that all the translationally invariant equilibrium states are a superposition of only two extremal states. [ABSTRACT FROM AUTHOR]

Copyright of Il Nuovo Cimento: A is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Il Nuovo Cimento: A is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The original publication of the article unfortunately contained a mistake in the first sentence of Theorem 1 and in the second part of the proof of Theorem 1. The corrected statement of Theorem as well as the corrected proof are given below. The full text of the corrected version is available at [ABSTRACT FROM AUTHOR]