Related papers: Extrapolation procedure for low-temperature series…
A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…
We present the results of Monte Carlo simulation for a Kondo lattice model in which itinerant electrons interact with Ising spins with spin-ice type easy-axis anisotropy on a pyrochlore lattice. We demonstrate the efficiency of the…
In the Ising model on the simple cubic lattice, we describe the inverse temperature $\beta$ and other quantities relevant for the computation of critical quantities in terms of a dimensionless squared mass $M$. The critical behaviors of…
From a consideration of high temperature series expansions in ferromagnets and in spin glasses, we propose an extended scaling scaling scheme involving a set of scaling formulae which express to leading order the temperature (T) and the…
We investigate the finite-temperature corrections to scaling in the three-state square-lattice Potts antiferromagnet, close to the critical point at T=0. Numerical diagonalization of the transfer matrix on semi-infinite strips of width $L$…
We report on a theoretical investigation of artificial spin-ice dipolar arrays, using a nanoisland geometry adopted from recent experiments [A. Farhan \textit{et al.}, Nature Phys.\ \textbf{9} (2013) 375]. The number of thermal magnetic…
Form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary disposition of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions ($N$) is…
In this work, the susceptibility of the square lattice Ising model is investigated using the recently obtained average magnetization interrelation, which is given by $\langle\sigma_{0, i}\rangle=…
The behavior of the compensation temperature of a mixed Ising ferrimagnetic system on a square lattice in which the two interpenetrating square sublattices have spins $\sigma$ ($\pm 1/2$) and spins $S$ ($\pm 1,0$) has been studied with…
We calculate very long low- and high-temperature series for the susceptibility $\chi$ of the square lattice Ising model as well as very long series for the five-particle contribution $\chi^{(5)}$ and six-particle contribution $\chi^{(6)}$.…
A new algorithm for the derivation of low-density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems. Numerical evidence shows that the computational complexity grows…
Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices…
The partition function of the square lattice Ising model on the rectangle with open boundary conditions in both directions is calculated exactly for arbitrary system size $L\times M$ and temperature. We start with the dimer method of…
We show that by means of connected-graph expansions one can effectively generate exact high-order series expansions which are informative of low-lying excited states for quantum many-body systems defined on a lattice. In particular, the…
We develop a diagrammatic approach for calculating the high temperature expansion of dynamic correlation functions, such as the electron Green's function and the time-dependent density-density and spin-spin correlation functions, for the…
The calculation of one loop integrals at finite temperature requires the evaluation of certain series, which converge very slowly or can even be divergent. Here we review a new method, recently devised by the author, for obtaining…
The Ising model at inverse temperature $\beta$ and zero external field can be obtained via the Fortuin-Kasteleyn (FK) random-cluster model with $q=2$ and density of open edges $p=1-e^{-\beta}$ by assigning spin +1 or -1 to each vertex in…
We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for…
We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and $Z(N<5)$ models. It also…
A new finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature of anisotropic two-layer Ising ferromagnet, on strips of r wide sites of square lattices. The reduced internal energy…