Related papers: The square lattice Ising model on the rectangle I:…
We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D…
Systems with an O(n) symmetrical Hamiltonian are considered in a $d$-dimensional slab geometry of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$. The…
We study the dimer and Ising models on a finite planar weighted graph with periodic-antiperiodic boundary conditions, i.e. a graph $\Gamma$ in the Klein bottle $K$. Let $\Gamma_{mn}$ denote the graph obtained by pasting $m$ rows and $n$…
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…
In this article, we study the finite temperature Casimir effect for scalar field with Robin boundary conditions on two parallel plates in a background spacetime that has a compact internal manifold with arbitrary geometry. The finite…
It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…
We derive low-temperature series (in the variable $u = \exp[-\beta J/S^2]$) for the spontaneous magnetisation, susceptibility and specific heat of the spin-$S$ Ising model on the square lattice for $S=\frac32$, 2, $\frac52$, and 3. We…
We consider systems confined to a $d$-dimensional slab of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$ and are describable by an O(n) symmetrical…
The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function $W$ of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the…
We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense,…
The Casimir friction problem for a pair of dielectric particles in relative motion is analyzed, utilizing a microscopic model in which we start from statistical mechanics for harmonically oscillating particles at finite temperature moving…
A scheme for measuring complex temperature partition functions of Ising models is introduced. In the context of ordered qubit registers this scheme finds a natural translation in terms of global operations, and single particle measurements…
We show that the vacuum ground state energy for massive scalars on a 1-dim L-sites periodic lattice can be interpreted as the thermodynamic free energy of particles at temperature 1/L governed by the Arutyunov-Frolov mirror Hamiltonian.…
The spin - 3/2 Ising model on a square lattice is investigated. It is shown that this model is reducible to an eight - vertex model on a surface in the parameter space spanned by coupling constants J, K, L and M. It is shown that this model…
This paper is a second in a series devoted to the study of a two-oscillator system in linear relative motion (the first one published as a letter in Europhys. Lett. 91, 60003 (2010)). The main idea behind considering this kind of system is…
The solvation force for the 2D Ising strip is calculated via exact diagonalization of the transfer matrix in two cases: the symmetric case corresponds to identical surface fields, and the antisymmetric case to exactly opposite surface…
The Casimir effect at finite temperature is investigated for a dilute dielectric ball; i.e., the relevant internal and free energies are calculated. The starting point in this study is a rigorous general expression for the internal energy…
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…
We explore short-distance static correlation functions in the infinite XXZ chain using previously derived formulae which represent the correlation functions in factorized form. We compute two-point functions ranging over 2, 3 and 4 lattice…
We consider the general $\mathbb{Z}_2$-symmetric free-fermion model on the finite periodic lattice, which includes as special cases the Ising model on the square and triangular lattices and $\mathbb{Z}_n$-symmetric BBS $\tau^{(2)}$-model…