Ising model on mixed two-dimensional lattices

We inform results on physical and topological magnitudes related to the ground level of Ising model on mixed two-dimensional lattices of coordination numbers 4 (Kagomé lattices) and 5 (five-point star lattices). We consider little clusters of size N, where N represents the total number of spins, subject to periodic boundary conditions. On these systems we randomly distribute ±J nearest-neighbor interactions (+J: antiferromagnetic, −J: ferromagnetic (F)). Concentration x of F interactions is varied in the interval (0,1). Two different methods are used to obtain results reported here. First, a numerical method related to multiple replicas. Second, an analytical method based on probabilistic analysis of flat and curved plaquettes. Both methods are complementary to each other. Initially, this study is restricted to calculate frustration of plaquettes and bonds, energy and bond order parameter at T=0. The results of magnitudes informed here are compared with the similar ones obtained for honeycomb, square and triangular lattices.     

Finite Size Corrections for the Ising Model on Higher Genus Triangular Lattices

We study the topology dependence of the finite size corrections to the Ising model partition function by considering the model on a triangular lattice embedded on a genus two surface. At criticality we observe a universal shape dependent correction, expressible in terms of Riemann theta functions, that reproduces the modular invariant partition function of the corresponding conformal field theory. The period matrix characterizing the moduli parameters of the limiting Riemann surface is obtained by a numerical study of the lattice continuum limit. The same results are reproduced using a discrete holomorphic structure.     

Magnetic properties and thermodynamics of decorated Ising chain with pendants of arbitrary spin

The decorated Ising chain with pendants of arbitrary spin and the single-ion anisotropy is exactly solved by the transfer matrix method. The solutions reveal abundant novel properties than the conventional one-dimensional Ising model. It is compared with the experimental data of a necklace-like molecule-based magnet, that gives a qualitative consistency.     

Phase diagram of a diluted triangular lattice Ising antiferromagnet in a field

Magnetization processes and phase transitions in a geometrically frustrated triangular lattice Ising antiferromagnet in the presence of an external magnetic field and a random site dilution are studied by the use of an effective-field theory with correlations. We find that the interplay between the applied field and the frustration-relieving dilution results in peculiar phase diagrams in the temperature-field-dilution parameter space.     

A candidate for a single‐chain magnet: [Mn3(OAc)6(py)2(H2O)2]n (OAc is acetate and py is pyridine)

The title complex, catena‐poly[di‐μ₃‐acetato‐κ⁶O:O:O′‐tetra‐μ₂‐acetato‐κ⁴O:O;κ⁴O:O′‐diaquabis(pyridine‐κN)trimanganese(II)], [Mn₃(CH₃COO)₆(C₆H₅N)₂(H₂O)₂]_n, is a true one‐dimensional coordination polymer, in which the Mn^II centres form a zigzag chain along [010]. The asymmetric unit contains two metal centres, one of which (Mn1) lies on an inversion centre, while the other (Mn2) is placed close to an inversion centre on a general position. Since all the acetates behave as bridging ligands, although with different μ₂‐ and μ₃‐coordination modes, a one‐dimensional polymeric structure is formed, based on trinuclear repeat units (Mn1...Mn2...Mn2′), in which the Mn2 and Mn2′ sites are related by an inversion centre. Within this monomeric block, the metal–metal separations are Mn1...Mn2 = 3.36180 (18) Å and Mn2...Mn2′ = 4.4804 (3) Å. Cation Mn1, located on an inversion centre, displays an [MnO₆] coordination sphere, while Mn2, on a general position, has a slightly stronger [MnO₅N] ligand field, as the sixth coordination site is occupied by a pyridine molecule. Both centres approximate an octahedral ligand field. The chains are parallel in the crystal structure and interact via hydrogen bonds involving coordinated water molecules. However, the shortest metal–metal separation between two chains [5.3752 (3) Å] is large compared with the intrachain interactions. These structural features are compatible with a single‐chain magnet behaviour, as confirmed by preliminary magnetic studies.     

随机横场与晶场作用混合自旋系统的热力学性质

利用有效场理论和切断近似,在伊辛模型的框架内考虑随机横场与晶场作用的混合自旋1/2 和自旋1系统的热力学性质。重点研究了晶场、横场和随机浓度对混合自旋系统相变的影响 ,研究发现在随机横场条件下,较小的晶场存在并不能改变临界横场阈值;取较大横场值时 在某些随机浓度的范围内出现重入相变现象,而取较小横场值时则没有出现重入相变现象。 给出了有关相图并进行了讨论。关键词：混合自旋系统伊辛模型热力学性质随机横场     

The Ising--Sherrington-Kirpatrick Model in a Magnetic Field at High Temperature

We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the limit of an infinite box. When both Ising and Sherrington-Kirpatrick temperatures are high enough, we prove that: (ii) the value of the pressure is given by a suitable replica symmetric solution, and (iii) the fluctuations of the pressure are of order of the inverse of the square of the volume with a normal distribution in the limit. In this regime, the pressure can be expressed in terms of random field Ising models.     

The analytic structure of lattice models — why can’t we solve most models?

We investigate the solvability of a variety of well-known problems in lattice statistical mechanics. We provide a new numerical procedure which enables one to conjecture whether the solution falls into a class of functions calleddifferentiably finite functions. Almost all solved problems fall into this class. The fact that one can conjecture whether a given problem is or is not D-finite then informs one as to whether the solution is likely to be tractable or not. We also show how, for certain problems, it is possible to prove that the solutions are notD-finite, based on the work of Rechnitzer [1–3].