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The extended Hubbard model in the atomic limit, which is equivalent to lattice $S=1/2$ fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard $U$ interaction and both nearest-neighbor ($W_{1}$) and next-nearest-neighbor ($W_{2}$) density-density intersite interactions. The variational approach treating the $U$ term exactly and the $W_l$ terms in the mean-field approximation is used to investigate thermodynamics of the model and to find its finite temperature ($T>0$) phase diagrams (as a function of particle concentration) for $W_{1}>0$ and $W_{2}0$. The evolution of the diagrams with increasing of $|W_{2}|/W_{1}$ is investigated. It is found that some of the PS states are stable only at $T>0$. Two different critical values of $|W_{2}|/W_{1}$ are determined for the PS states, in which two ordered phases of the same type (i.e., two domains of the DCO or TCO phase) coexist., 7 pages, 5 figures, 57 references; pdf-RevTeX class used. This is the author created version of an article accepted for publication in J. Magn. Magn. Matter (Elsevier) journal. The article has been published on a gold open access basis under a CC BY 4.0 licence

We present studies of an effective model which is a simple generalization of the standard model of a local pair superconductor with on-site pairing (i.e., the model of hard core bosons on a lattice) to the case of finite pair binding energy. The tight binding Hamiltonian consists of (i) the effective on-site interaction U, (ii) the intersite density-density interactions W between nearest-neighbours, and (iii) the intersite charge exchange term I, determining the hopping of electron pairs between nearest-neighbour sites. In the analysis of the phase diagrams and thermodynamic properties of this model we treat the intersite interactions within the mean-field approximation. Our investigations of the U0 case show that, depending on the values of interaction parameters, the system can exhibit three homogeneous phases: superconducting (SS), charge-ordered (CO) and nonordered (NO) as well as the phase separated SS-CO state., 4 pages, 3 figures; pdf-ReVTeX; Submitted to: JOURNAL OF SUPERCONDUCTIVITY AND NOVEL MAGNETISM; presented also at PHASE SEPARATION AND SUPERSTRIPES in high temperature superconductors and related materials - SUPERSTRIPES (2012) - 55th Conference of INTERNATIONAL SCHOOL OF SOLID-STATE PHYSICS, Ettore Majorana Foundation, Centre for Scientific Culture, Erice - Italy: July 11-17, 2012

This is an author-created, un-copyedited version of an article accepted for publication in Acta Physica Polonica A. In this work the extended Hubbard models with pair hopping interaction (at the atomic limit) are investigated within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation (exact in $d\rightarrow+\infty$). We analyze mutual stability of the superconducting (SC) phase and charge (CO) or (ferro/antiferro-)magnetic (M) orderings as well as homogeneous mixed phases. Our preliminary results for U=0 show that the SC phase can coexist with the CO or M phases only in states with electron phase separation. National Science Center (NCN) as a research project in years 2011-2013, under grant No. DEC-2011/01/N/ST3/00413; National Science Center (NCN) as a doctoral scholarship in years 2013-2014 No. DEC- 2013/08/T/ST3/00012; European Commission and Ministry of Science and Higher Education (Poland) - partial financial support from European Social Fund – Operational Programme "Human Capital" – POKL.04.01.01-00-133/09-00 – "Proinnowacyjne kształcenie, kompetentna kadra, absolwenci przyszłości"

In this work we focus on the study of phase separation in the zero-bandwidth extended Hubbard with nearest-neighbors intersite Ising-like magnetic interactions $J$ and on-site Coulomb interactions $U$. The system has been analyzed by means of Monte Carlo simulations (in the grand canonical ensemble) on two dimensional square lattice (with $N=L\times L =400$ sites) and the results for $U/(4J)=2$ as a function of chemical potential and electron concentration have been obtained. Depending on the values of interaction parameters the system exhibits homogeneous (anti-)ferromagnetic (AF) or non-ordered (NO) phase as well as phase separation PS:AF/NO state. Transitions between homogeneous phases (i.e. AF-NO transitions) can be of first or second order and the tricritical point is also present on the phase diagrams. The electron compressibility $K$ is an indicator of the phase separation and that quantity is of particular interest of this paper., Comment: 4 pages, 3 figures; pdf-ReVTeX; updated references; presented at The European Conference PHYSICS OF MAGNETISM 2014 (PM'14), June 23-27, 2014, Poznan, Poland; submitted to Acta Physica Polonica A

The lack of the experimental evidence and doing of the similar examinations” are two reasons for some experimental scientists to state that the causality principle is not valid at the atomic limit. In this paper these two reasons are investigated and we show that if the causality or the rational rules are ignored for solving the problem which we faced with (i.e. according to rationality rules we believe that the causality principle is valid at the atomic limit, and on the other hand, we have not found any experimental evidence for this principle) then the process of inquiry would be stopped. But if we reject the other cases, we don’t have this problem.

We consider the spin and pseudospin (charge) response functions of the exactly soluble Anderson atom model. We demonstrate, in particular, that a deviation from the magnetic Curie-law behaviour, appropriate for a free spin one-half, increases with increasing asymmetry and temperature. In general, oscillator strength is transferred from the spin degrees of freedom to the pseudospin modes. We also consider the negative-U Anderson atom and demonstrate that the pseudospin modes are the relevant low-energy excitations in this case. Especially, the roles of the spin and charge excitations are interchanged upon reversal of the intrasite Coulomb repulsion, U., 23 pages, 12 figures. Accepted for publication in J. Low Temp. Phys

We have studied a simple effective model of charge ordered insulators. The tight binding Hamiltonian consists of the effective on-site interaction U and the intersite density-density interaction Wij (both: nearest-neighbor and next-nearest-neighbor). In the analysis of the phase diagrams and thermodynamic properties of this model we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigations of the general case (as a function of the electron concentration) have shown that the system exhibits various critical behaviors including among others bicritical, tricritical, critical-end and isolated critical points. In this report we concentrate on the metastable phases and transitions between them. One finds that the first- and second order transitions between metastable phases can exist in the system. These transitions occur in the neighborhood of first as well as second order transitions between stable phases. For the case of on-site attraction the regions of metastable homogeneous phases occurrence inside the ranges of phase separated states stability have been also determined., 3 pages, 3 figures, pdf-ReVTeX, presented at The European Conference PHYSICS OF MAGNETISM 2011, June 27 - July 1, 2011, Pozna\'n, POLAND

In this paper the two dimensional extended Hubbard model with intersite magnetic Ising-like interaction in the atomic limit is analyzed by means of the classical Monte Carlo method in the grand canonical ensemble. Such an effective simple model could describe behavior of insulating (anti)ferromagnets. In the model considered the Coulomb interaction ($U$) is on-site and the magnetic interactions in $z$-direction ($J>0$, antiferromagnetic) are restricted to nearest-neighbors. Simulations of the model have been performed on a square lattice consisting of $N=L\times L=400$ sites ($L=20$) in order to obtain the full phase diagram for $U/(4J)=1$. Results obtained for on-site repulsion ($U>0$) show that, apart from homogeneous non-ordered (NO) and ordered magnetic (antiferromagnetic, AF) phases, there is also a region of phase separation (PS: AF/NO) occurrence. We present a phase diagram as well as some thermodynamic properties of the model for the case of $U/(4J)=1$ (and arbitrary chemical potential and arbitrary electron concentration). The AF-NO transition can be second-order as well as first-order and the tricritical point occurs on the diagram., 5 pages, 4 figures, pdf-ReVTeX, presented at 16th National School of Superconductivity: Unconventional superconductivity and strongly correlated systems, Zakopane, Poland, October 7-12, 2013, submitted to Acta Physica Polonica A

We present studies of the atomic limit of the extended Hubbard model with pair hopping for arbitrary electron density and arbitrary chemical potential. The Hamiltonian consists of (i) the effective on-site interaction $U$ and (ii) the intersite charge exchange term $I$, determining the hopping of electron pairs between nearest-neighbour sites. In the analysis of the phase diagrams and thermodynamic properties of this model we treat the intersite interactions within the mean-field approximation. In this report we focus on metastable phases and determine their ranges of occurrence. Our investigations in the absence of the external magnetic field show that the system analysed exhibits tricritical behaviour. Two metastable phases (superconducting and nonordered) can exist inside the regions of the phase separated state stability and a first-order transition occurs between these metastable phases., Comment: 5 pages, 3 figures; pdf-ReVTeX; submitted to: Journal of Superconductivity and Novel Magnetism

We present the analysis of paramagnetic effects of magnetic field ($B$) (Zeeman term) in the zero-bandwidth limit of the extended Hubbard model for arbitrary chemical potential $\mu$ and electron density $n$. The effective Hamiltonian considered consists of the on-site interaction $U$ and the intersite charge exchange term $I$, determining the hopping of electron pairs between nearest-neighbour sites. The model has been analyzed within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation (rigorous in the limit of infinite dimensions $d\rightarrow+\infty$). In this report we focus on metastable phases as well as phase separated (PS) states involving superconducting (SS) and nonordered (NO) phases and determine their ranges of occurrence for $U/I_0=1.05$ ($I_0=zI$) in the presence of magnetic field $B\neq0$. Our investigations of the general case for arbitrary $U/I_0$ show that, depending on the values of interaction parameters (for fixed $n$), the PS state can occur in higher fields than the homogeneous SS phase (field-induced PS). Moreover, a first-order SS-NO transition occurs between metastable phases and these metastable phases can exist inside the regions of the PS state stability. Such behaviour is associated with the presence of tricritical line on the phase diagrams of the system., Comment: 6 pages, 3 figures; pdf-ReVTeX; presented at 16th National School of Superconductivity: Unconventional superconductivity and strongly correlated systems, Zakopane, Poland, October 7-12, 2013; submitted to Acta Physica Polonica A

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential and focus on paramagnetic effects of the external magnetic field. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach (VA), which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case shows that the system can exhibit not only the homogeneous phases: superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). Depending on the values of interaction parameters, the PS state can occur in higher fields than the SS phase (field-induced PS). Some ground state results beyond the VA are also presented., Comment: 9 pages, 6 figures, 1 table; pdf-ReVTeX; This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics: Condensed Matter. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. arXiv admin note: substantial text overlap with arXiv:1203.5805

In this report we have analyzed a simple effective model for a description of magnetically ordered insulators. The Hamiltonian considered consists of the effective on-site interaction (U) and the intersite Ising-like magnetic exchange interaction (J) between nearest neighbors. For the first time the phase diagrams of this model have been determined within Monte Carlo simulation on 2D-square lattice. They have been compared with results obtained within variational approach, which treats the on-site term exactly and the intersite interactions within mean-field approximation. We show within both approaches that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic (F) and nonordered (NO), but also phase separated states (PS: F-NO)., 4 pages, 4 figures, pdf-ReVTeX, presented at The European Conference Physics of Magnetism 2011, June 27 - July 1, 2011, Poznan, Poland

The local structure in high temperature superconductors is nowadays considered a key point for understanding superconductivity mechanism. MgB2 has a well-known simple structure; but its local structure remains quite unexplored. This is due to the fact that typical x-ray local probes, such as EXAFS, fail when used to study local structure of light atoms, such as Mg and B. We used high resolution neutron diffraction with pair distribution function (PDF) analysis for investigating disorder on the atomic scale in the Al doped Mg1-xAlxB2 system. The results indicate an anisotropic structural inhomogeneity along the c-axis that could be related with the delocalized metallic-type bonding between Boron layers., Comment: Campi, G., Ricci, A., & Bianconi, A. (2012). Local structure in mg1-x al x b2 system by high resolution neutron diffraction. Journal of Superconductivity and Novel Magnetism

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d=1) in the ground state. Moreover, at T=0 some results derived within the random phase approximation (and the spin-wave approximation) for d=2 and d=3 lattices and within the low density expansions for d=3 lattices are presented. Our investigation of the general case (as a function of the electron concentration and as a function of the chemical potential) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases: superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points., Comment: 15 pages, 9 figures; pdf-ReVTeX, final version, corrected typos; submitted to Journal of Physics: Condensed Matter

We present our preliminary studies of an effective model of a superconductor with short coherence length involving magnetic interactions. The Hamiltonian considered consists of (i) the effective on-site interaction U, (ii) the intersite magnetic exchange interactions (Jz, Jxy) between nearest-neighbors and (iii) the intersite charge exchange term I, determining the hopping of electron pairs between nearest-neighbor sites. In the analysis of the phase diagrams and thermodynamic properties of this model for half-filling (n=1) we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. One finds that the system considered can exhibit very interesting multicritical behaviors (including tricritical, critical-end and bicritical points) caused by the competition between magnetism and superconductivity, even for n=1. Our investigations show that, depending on the values of interaction parameters, the system at half-filling can exhibit three homogeneous phases: superconducting (SS), (anti-)ferromagnetic (F) and nonordered (NO). The transitions between ordered phases (SS, F) and the NO phase can be first order as well as second order ones, whereas SS-F transition is first order one. Temperature dependencies of the order parameters and thermodynamic properties of the system at the sequence of transitions: SS-F-NO with increasing temperature for J/I=0.3, U/I0 = 0.69 and n=1 are also presented., 5 pages, 3 figures, presented at 15th National School of Superconductivity - 100 years of superconductivity, Kazimierz Dolny, Poland, October 9 - 13, 2011; final version, pdf-ReVTeX, corrected typos

A simple effective model of charge ordered and (or) magnetically ordered insulators is studied. The tight binding Hamiltonian analyzed consists of (i) the effective on-site interaction U, (ii) the intersite density-density interaction W and (iii) intersite magnetic exchange interaction Jz (or Jxy) between nearest-neighbors. The intersite interaction are treated within the mean-field approximation. One shows that the systems considered can exhibit very interesting multicritical behaviors, including among others bicritical, tricritical, tetracritical and critical end points. The analysis of the model has been performed for an arbitrary electron concentration as well as an arbitrary chemical potential in the limit of strong on-site repulsion. The phase diagrams obtained in such a case are shown to consist of at least 9 different states, including four homogenous phases: nonordered (NO), ferromagnetic (F), charge ordered (CO), ferrimagnetic (intermediate, I) and five types of phase separation: NO-NO, F-NO, F-F, CO-F, CO-I., 3 pages, 5 figures, pdf-ReVTeX, presented at The European Conference Physics of Magnetism 2011, June 27 - July 1, 2011, Poznan, Poland

We have studied the extended Hubbard model in the atomic limit. The Hamiltonian analyzed consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). The model can be considered as a simple effective model of charge ordered insulators. The phase diagrams and thermodynamic properties of this system have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. Our investigation of the general case taking into account for the first time the effects of longer-ranged density-density interaction (repulsive and attractive) as well as possible phase separations shows that, depending on the values of the interaction parameters and the electron concentration, the system can exhibit not only several homogeneous charge ordered (CO) phases, but also various phase separated states (CO-CO and CO-nonordered). One finds that the model considered exhibits very interesting multicritical behaviours and features, including among others bicritical, tricritical, critical-end and isolated critical points., 12 pages, 7 figures; final version, pdf-ReVTeX; corrected typos in reference; submitted to Journal of Physics: Condensed Matter

A simple effective model of charge ordered insulators is studied. The tight binding Hamiltonian consists of the effective on-site interaction U and the intersite density-density interactions Wij (both: nearest-neighbour and next-nearest-neighbour). In the analysis of the phase diagrams we have adopted the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. The phase separated states have not been taken into account in previous analyses. Our investigations of two cases of the on-site interaction: attraction (U/(-W_Q)=-10) and repulsion (U/(-W_Q)=1.1) show that, depending on the values of the next-nearest-neighbour attraction, the system can exhibit not only homogeneous phases: charge ordered (CO) and nonordered (NO), but also various phase separated states (CO--NO, CO--CO)., Comment: 3 pages, 2 figures, presented at the 14th National School of Superconductivity - Superconductivity and heterogeneous condensed systems, Ostrow Wielkopolski, Poland, October 13-17, 2009; final version, pdf-ReVTeX, corrected typos

A simple effective model for a description of magnetically ordered insulators is analysed. The tight binding Hamiltonian consists of the effective on-site interaction (U) and intersite magnetic exchange interactions (Jz, Jxy) between nearest-neighbours. The phase diagrams of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We show that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic (F) and nonordered (NO), but also phase separated states (PS: F-NO)., Comment: 3 pages, 3 figures, presented at the 14th National School of Superconductivity - Superconductivity and heterogeneous condensed systems, Ostrow Wielkopolski, Poland, October 13-17, 2009; final version, pdf-ReVTeX, corrected typos

This is an author-created, un-copyedited version of an article accepted for publication in Journal of Superconductivity and Novel Magnetism. We present the ground state results for lattice models of superconductor (SC) with extremely short coherence length, which also involve the interplay with charge (CO) and (anti-)ferromagnetic orderings. Our preliminary results at zero-temperature (derived by means of the variational approach which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation, exact in $d\rightarrow+\infty$), yields that the SC phase can coexist with the CO or magnetic (M) phases in states with electron phase separation (PS:SC/CO and PS:SC/M, respectively). National Science Center (NCN) as a research project in years 2011-2013, under grant No. DEC-2011/01/N/ST3/00413; European Commission and Ministry of Science and Higher Education (Poland) - partial financial support from European Social Fund – Operational Programme "Human Capital" – POKL.04.01.01-00-133/09-00 – "Proinnowacyjne kształcenie, kompetentna kadra, absolwenci przyszłości"; National Science Center (NCN) as a doctoral scholarship in years 2013-2014, No. DEC- 2013/08/T/ST3/00012; The Fundation of Adam Mickiewicz University in Poznań