An exact solution on the ferromagnetic Face-Cubic spin model on a Bethe lattice

Simple cubic lattice (SC lattice) can be viewed as plane triangular lattice (PT lattice) by viewing it along its principle diagonal lines. By viewing thus we establish the exact one-to-one correspondence between the closed graphs on SC lattice and the corresponding closed graphs on PT lattice. We thus see that the propagator for PT lattice (with suitable modifications) can be used to solve, at least in principle, the 3D Ising problem for SC lattice in the absence of external ...

We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices that are created automatically based on the structure of the system. By generalizing this method, it becomes possible to calculate the partition function of various crystal systems (network shapes) in magnetic fields when N (scale) is infinite...

New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of the finite lattice method but also to the standard graphical method. It is applied to extend the high-temperature series of the simple cubic Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25} to beta^{32} for th...

We present a detailed study of the ground state phase diagram of the classical frustrated Heisenberg model on the face-centered-cubic lattice. By considering exchange interactions up till third nearest neighbors, we find commensurate, helimagnetic, as well as noncollinear multi-{\bf Q} orders which include noncoplanar and chiral spin structures. We reveal the presence of subextensively degenerate manifolds that appear at triple points and certain phase boundaries in the phase...

A closed-form exact analytical solution for the q-state Potts model on a ladder 2 x oo with arbitrary two-, three-, and four-site interactions in a unit cell is presented. Using the obtained solution it is shown that the finite-size internal energy equation yields an accurate value of the critical temperature for the triangular Potts lattice with three-site interactions in alternate triangular faces. It is argued that the above equation is exact at least for self-dual models ...

We use large deviation theory to obtain the free energy of the XY model on a fully connected graph on each site of which there is a randomly oriented field of magnitude $h$. The phase diagram is obtained for two symmetric distributions of the random orientations: (a) a uniform distribution and (b) a distribution with cubic symmetry. In both cases, the disorder-averaged ordered state reflects the symmetry of the underlying distribution. The phase boundary has a multicritical p...

We review the exact results on the various critical regimes of the antiferromagnetic $Q$-state Potts model. We focus on the Bethe Ansatz approach for generic $Q$, and describe in each case the effective degrees of freedom appearing in the continuum limit.

In this work we deal with doubly decorated Ising-Heisenberg models on planar lattices. Applying the generalized decoration-iteration transformation we obtain exact results for the antiferromagnetic version of the model. The existence of a new quantum dimerized phase is predicted and its physical properties are studied and analyzed. Particular attention has been paid to the investigation of the phase boundaries, pair-correlation functions and specific heat. A possible applicat...

We show that the simple update approach proposed by Jiang et. al. [H.C. Jiang, Z.Y. Weng, and T. Xiang, Phys. Rev. Lett. 101, 090603 (2008)] is an efficient and accurate method for determining the infinite tree tensor network states on the Bethe lattice. Ground state properties of the quantum transverse Ising model and the Heisenberg XXZ model on the Bethe lattice are studied. The transverse Ising model is found to undergo a second-order quantum phase transition with a diverg...

The equations for the spontaneous magnetization for different three-dimensional lattices have been derived in a heuristic manner. The estimated critical temperatures for simple cubic, face-centered cubic, body-centered cubic and diamond lattices are in excellent agreement with recent computer simulation data.