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We analyse the probability distribution functions of the energy and magnetisation of the two-dimensional Blume-Capel and Baxter-Wu models with spin values $S \in \{1/2,1, 3/2\}$ in the presence of a crystal field $\Delta$. By employing extensive single-spin flip Monte Carlo simulations and a recently developed method of studying the zeros of the energy probability distribution we are able to probe, with a good numerical accuracy, several critical characteristics of the transitions. Additionally, the universal aspects of these transitions are scrutinised by computing the corresponding probability distribution functions. The energy distribution has been underutilised in the literature when compared to that of the magnetisation. Somewhat surprisingly, however, the former appears to be more robust in characterising the universality class for both models upon varying the crystal field $\Delta$ than the latter. Finally, our analysis suggests that in contrast to the Blume-Capel ferromagnet, the Baxter-Wu model appears to suffer from strong finite-size effects, especially upon increasing $\Delta$ and $S$, that obscure the application of traditional finite-size scaling approaches., Comment: 24 pages, 9 figures, 1 table, minor revised version accepted for publication in JSTAT

We investigate the critical behavior of the two-dimensional spin-$1$ Baxter-Wu model in the presence of a crystal-field coupling $\Delta$ with the goal of determining the universality class of transitions along the second-order part of the transition line as one approaches the putative location of the multicritical point. We employ extensive Monte Carlo simulations using two different methodologies: (i) a study of the zeros of the energy probability distribution, closely related to the Fisher zeros of the partition function, and (ii) the well-established multicanonical approach employed to study the probability distribution of the crystal-field energy. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the $(\Delta, T)$ phase diagram supports previous claims that the transition belongs to the universality class of the $4$-state Potts model. For positive values of $\Delta$, we observe the presence of strong finite-size effects, indicative of crossover effects due to the proximity of the first-order part of the transition line. Finally, we demonstrate how a combination of cluster and heat-bath updates allows one to equilibrate larger systems, and we demonstrate the potential of this approach for resolving the ambiguities observed in the regime of $\Delta \gtrsim 0$., Comment: 11 pages, 11 figures, 2 tables, new updated titled, version to be published in Phys Rev E

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior in the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale $L^{\ast} \approx 32$ for the chosen parameters., Comment: 6 pages, 4 figures, version to be published in Phys. Rev. E as a Rapid Communication

We review the pertinent features of the phase diagram of the zero-field Blume-Capel model, focusing on the aspects of transition order, finite-size scaling and universality. In particular, we employ a range of Monte Carlo simulation methods to study the 2D spin-1 Blume-Capel model on the square lattice to investigate the behavior in the vicinity of the first-order and second-order regimes of the ferromagnet-paramagnet phase boundary, respectively. To achieve high-precision results, we utilize a combination of (i) a parallel version of the multicanonical algorithm and (ii) a hybrid updating scheme combining Metropolis and generalized Wolff cluster moves. These techniques are combined to study for the first time the correlation length of the model, using its scaling in the regime of second-order transitions to illustrate universality through the observed identity of the limiting value of $\xi/L$ with the exactly known result for the Ising universality class., Comment: 16 pages, 7 figures, 1 table, submitted to Eur. Phys. J. Special Topics

Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly understood above the upper critical dimension $d_c$ in models with free boundary conditions. Besides its fundamental significance for scaling theories, the issue is important at a practical level because finite-size, statistical-physics systems, with free boundaries above $d_c$, are experimentally accessible with long-range interactions. Here we address the roles played by Fourier modes for such systems and show that the current phenomenological picture is not supported for all thermodynamic observables either with free or periodic boundaries. Instead, the correct picture emerges from a sector of the renormalization group hitherto considered unphysical., Comment: 10 pages, 2 figures

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at continuous phase transitions. Below the upper critical dimension, where the correlation length is proportional to the system length, both finite-size scaling and hyperscaling take conventional forms. Above the upper critical dimension these forms break down and a new scaling scenario appears. Here we investigate this scaling behaviour in one-dimensional Ising ferromagnets with long-range interactions. We show that the correlation length scales as a non-trivial power of the linear system size and investigate the scaling forms. For interactions of sufficiently long range, the disparity between the correlation length and the system length can be made arbitrarily large, while maintaining the new scaling scenarios. We also investigate the behavior of the correlation function above the upper critical dimension and the modifications imposed by the new scaling scenario onto the associated Fisher relation., Comment: 16 pages, 5 figures

We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations formulation of Euclidean quantum gravity in two dimensions. For regular lattices, it is well-established that at criticality the properties of Fortuin-Kasteleyn clusters are directly related to the conventional critical exponents, whereas the corresponding properties of the geometric clusters of like spins are not. Recently it has been observed that the latter are related to the critical properties of a tricritical Potts model with the same central charge. We apply the KPZ formalism to develop a related prediction for the case of Potts models coupled to quantum gravity and employ numerical simulation methods to confirm it for the Ising case q=2., Comment: 12 pages, 1 figure, 1 table

The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables, one thus obtains not only the critical exponents but even the corresponding amplitudes of the divergences analytically. A first numerical analysis brought up the question whether analogous results can be obtained for those systems on three-dimensional manifolds. Using Monte Carlo simulations based on the Wolff single-cluster update algorithm we investigate the scaling properties of O(n) symmetric classical spin models on a three-dimensional, hyper-cylindrical geometry with a toroidal cross-section considering both periodic and antiperiodic boundary conditions. Studying the correlation lengths of the Ising, the XY, and the Heisenberg model, we find strong evidence for a scaling relation analogous to the two-dimensional case, but in contrast here for the systems with antiperiodic boundary conditions., Comment: 4 pages, LaTeX, proceedings of the 210th WE-Heraeus Seminar PILS'98, Berlin

It is shown that the modern equations of state for neutron star matter based on microscopic calculations of symmetric and asymmetric nuclear matter are compatible with the lower bound on the maximum neutron-star mass for a certain range of hyperon coupling constants, which are constrained by the binding energies of hyperons in symmetric nuclear matter. The hyperons are included by means of the relativistic Hartree-- or Hartree--Fock approximation. The obtained couplings are also in satisfactory agreement with hypernuclei data in the relativistic Hartree scheme. Within the relativistic Hartree--Fock approximation hypernuclei have not been investigated so far., Comment: 12 pages, 3 figures. Dedicated to Prof. Georg Suessmann on the occasion of his 70th birthday. To be published in Zeitschrift fuer Naturforschung A

The effect of rotation on the cooling of neutron stars is investigated. The thermal evolution equations are solved in two dimensions with full account of general relativistic effects. It is found that rotation is particularly important in the early epoch when the neutron star's interior is not yet isothermal. The polar surface temperature is up to 63% higher than the equatorial temperature. This temperature difference might be observable if the thermal radiation of a young, rapidly rotating neutron star is detected. In the intermediate epoch (10^2 < t < 10^5 yr), when the interior becomes isothermal, the polar temperature is still up to 31% higher than the equatorial temperature. Afterwards photon surface radiation dominates the cooling, and the surface becomes isothermal on a timescale of 10^7 yr. Furthermore, the transition between the early and the intermediate epochs is delayed by several hundred years. An additional effect of rotation is the reduction of the neutrino luminosity due to the reduction of the central density with respect to the non-rotating case., Comment: 4 pages, 2 figures, to be published in letter section of Astronomy & Astrophysics

The possibility of a neutron m=2-superfluid in the interior of neutron stars is investigated. This pairing state is energetically favoured in strong magnetic fields ($H\sim 10^{16}-10^{17}$ G). Because of the node in the angular-dependent energy gap along the field direction the neutrino emissivity is only suppressed polynomially as function in $T/T_{c}$ instead of exponentially, as it is obtained for a nodeless pairing state. The effect of this pairing state on the thermal evolution of neutron stars is studied, and its outcome is compared with the evolution of ``normal'', i.e. nodeless, superfluid and non-superfluid neutron stars, and also with observations. We find that particularly the predicted surface temperatures of the enhanced cooling scenario considerably change and come into agreement with temperatures deduced from observational data within the hydrogen atmosphere model. Furthermore the surface temperature depends on the magnetic field strength as an additional parameter aside from the neutron star mass. The latter is however only operative in the case of the intermediate cooling scenario., Comment: 10 pages including 6 ps-figures. To be published in Astronomy & Astrophysics. Postscript version of paper and additional tables can be found at http://www.physik.uni-muenchen.de/sektion/suessmann/astro/cool/schaab.0797

The properties of hot matter are studied in the frame of the relativistic Brueckner-Hartree-Fock theory. The equations are solved self-consistently in the full Dirac space. For the interaction we used the potentials given by Brockmann and Machleidt. The obtained critical temperatures are smaller than in most of the nonrelativistic investigations. We also calculated the thermodynamic properties of hot matter in the relativistic Hartree--Fock approximation, where the force parameters were adjusted to the outcome of the relativistic Brueckner--Hartree--Fock calculations at zero temperature. Here, one obtains higher critical temperatures, which are comparable with other relativistic calculations in the Hartree scheme., Comment: 8 pages, 9 figures, submitted in a shorter version to Phys. Rev. C

We study the properties of neutron stars adopting relativistic equations of state of neutron star matter, calculated in the framework of the relativistic Brueckner-Hartree-Fock approximation for electrically charge neutral neutron star matter in beta-equilibrium. For higher densities more baryons (hyperons etc.) are included by means of the relativistic Hartree- or Hartree-Fock approximation. The special features of the different approximations and compositions are discussed in detail. Besides standard neutron star properties special emphasis is put on the limiting periods of neutron stars, for which the Kepler criterion and gravitation-reaction instabilities are considered. Furthermore the cooling behaviour of neutron stars is investigated, too. For comparison we give also the outcome for some nonrelativistic equations of state., Comment: 43 pages, 22 ps-figures, to be published in the International Journal of Modern Physics E

The general statement that strange stars cool more rapidly than neutron stars is investigated in greater detail. It is found that the direct Urca process could be forbidden not only in neutron stars but also in strange stars. If so, strange stars would be slowly cooling and their surface temperatures would be more or less indistinguishable from those of slowly cooling neutron stars. The case of enhanced cooling is reinvestigated as well. It is found that strange stars cool significantly more rapidly than neutron stars within the first $\sim 30$ years after birth. This feature could become particularly interesting if continued observation of SN 1987A would reveal the temperature of the possibly existing pulsar at its centre., Comment: 10 pages, 3 ps-figures, to appear in the proceedings of the International Symposium on ''Strangeness in Quark Matter 1997``, April 14--18, Thera (Santorini), Hellas

This paper gives an overview of the properties of all possible equilibrium sequences of compact strange-matter stars with nuclear crusts, which range from strange stars to strange dwarfs. In contrast to their non-strange counterparts, --neutron stars and white dwarfs--, their properties are determined by two (rather than one) parameters, the central star density and the density at the base of the nuclear crust. This leads to stellar strange-matter configurations whose properties are much more complex than those of the conventional sequence. As an example, two generically different categories of stable strange dwarfs are found, which could be the observed white dwarfs. Furthermore we find very-low-mass strange stellar objects, with masses as small as those of Jupiter or even lighter planets. Such objects, if abundant enough in our Galaxy, should be seen by the presently performed gravitational microlensing searches., Comment: 15 pages, LaTeX, plus 9 postscript figures. Presented by F. Weber at the Vulcano Workshop 1996 Frontier Objects in Astrophysics and Particle Physics May 27 -- June 1, Vulcano, Italy. To be published by the Societa Italiana di Fisica

Neutrino emission from the dense hadronic component in neutron stars is subject to strong modifications due to collective effects in the nuclear medium. We implement new estimates of the neutrino emissivities of two processes operating in the nuclear medium into numerical cooling simulations of neutron stars. The first process is the modified Urca process, for which the softening of the pion exchange mode and other polarization effects as well as the neutrino emission arising from the intermediate reaction states are taken into account. The second process concerns neutrino emission through superfluid pair breaking and formation processes. It is found that the medium effects on the emissivity of the modified Urca process result in a strong density dependence, which gives a smooth crossover from the standard to the nonstandard cooling scenario for increasing star masses. For superfluid stars, the superfluid pair breaking and formation processes accelerate mildly both the standard and the nonstandard cooling scenario. This leads to a good agreement between the theoretical cooling tracks and the rather low temperatures observed for objects like PSRs 0833-45 (Vela), 0656+14, and 0630+18 (Geminga). The robustness of our findings against variations in both the underlying equation of state of baryonic matter and the used fast cooling processes is demonstrated. Hence we conclude that the two recalculated neutrino emissivities studied here enable one to reproduce theoretically most of the observed pulsar temperatures by varying the masses of neutron star models., Comment: 31 pages (LaTex) including 15 ps-figures, revised version, to be published in Astronomy and Astrophysics

This paper gives an overview of the properties of all possible equilibrium sequences of compact strange-matter stars with nuclear crusts, which range from strange stars to strange dwarfs. In contrast to their non-strange counterparts, --neutron stars and white dwarfs--, their properties are determined by two (rather than one) parameters, the central star density and the density at the base of the nuclear crust. This leads to stellar strange-matter configurations whose properties are much more complex than those of the conventional sequence. As an example, two generically different categories of stable strange dwarfs are found, which could be the observed white dwarfs. Furthermore we find very low-mass strange stellar objects, with masses as small as those of Jupiter or even lighter planets. Such objects, if abundant enough in our Galaxy, should be seen by the presently performed gravitational microlensing searches. Further aspects studied in this paper concern the limiting rotational periods and the cooling behavior of neutron stars and their strange counterparts., Comment: 9 pages, 3 figures

A collection of modern, field-theoretical equations of state is applied to the investigation of cooling properties of compact stars. These comprise neutron stars as well as hypothetical strange matter stars, made up of absolutely stable 3-flavor strange quark matter. Various uncertainties in the behavior of matter at supernuclear densities, e.g., hyperonic degrees of freedom, behavior of coupling strengths in matter, pion and meson condensation, superfluidity, transition to quark matter, absolute stability of strange quark matter, and last but not least the many-body technique itself are tested against the body of observed cooling data., Comment: 41 pages, revised version

Single--particle spectra of $\Lambda $ and $\Sigma $ hypernuclei are calculated within a relativistic mean--field theory. The hyperon couplings used are compatible with the $\Lambda $ binding in saturated nuclear matter, neutron-star masses and experimental data on $\Lambda $ levels in hypernuclei. Special attention is devoted to the spin-orbit potential for the hyperons and the influence of the $\rho $-meson field (isospin dependent interaction)., Comment: 18 pages, including 2 figs., figs. 1 and 4-6 available as postscript-datasets on request; written in Latex, report# LBL-33031