The boundary condition dependence of the correlation functions in a phase transition region of the thermodynamic parameters is of great importance to understand the character and properties of the phase transition itself. In this paper we study the boundary condition dependence of certain correlation functions in the Ising model at low temperature. § 1. Motivation of the Paper. A Related Proble...

We conjecture the existence of hidden Onsager algebra symmetries in two interacting quantum integrable lattice models, i.e. spin-1/2 XXZ model and spin-1 Zamolodchikov-Fateev at arbitrary root unity values anisotropy. The conjectures relate generators to conserved charges obtained from semi-cyclic transfer matrices. are motivated by examples which XX U(1)-invariant clock model. A novel construc...

We discuss the problem of the equivalence between continuous-time random walk (CTRW) and generalized master equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution density psi(t) that is assumed to be an inverse power law with the power index micro. We assume that the Onsager p...

A zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a quasi-periodic distribution of up to eight different coupling constants. The duality transformation on this tiling is considered and the self-dual couplings are determined. Furthermore, we analyze the s...

The Onsager reaction term is one of the most important notions for frustrated random systems. The role of the Onsager reaction term, however, has not been properly elucidated for non-equilibrium random systems with large degrees of freedoms. By analyzing oscillator associative memory models involving two types of diluted couplings, we make clear that the acceleration (deceleration) effect is ca...

Finite thermostats are studied in the context of nonequilibrium statistical mechanics. Entropy production rate has been identified with the mechanical quantity expressed by the phase space contraction rate and the currents have been linked to its derivatives with respect to the parameters measuring the forcing intensities. In some instances GreenKubo formulae, hence Onsager reciprocity, have be...

The diffusive motion of foreign particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids a...

The quantum kinetic equation for charged particles in strong electric fields is used to derive the nonlinear particle flux. The relaxation field is calculated quantum mechanically up to any order in the applied field provided a given Maxwellian plasma. The classical limit is given in analytical form. In the range of weak fields the deformation of the screening cloud is responsible for the Debye...