Hiroaki Arisue

Algorithm of the finite-lattice method for high-temperature expansion of the Ising model in three dimensions

We propose an algorithm of the finite-lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple-cubic lattice from the previous series of 26th order to 46th order in the inverse temperature. The obtained series give the estimate of the critical exponent for the specific heat in high precision.

Generalized Schrödinger representation and its application to gauge field theories

A generalization of the Schrodinger representation is presented and applied to theories with indefinite metric as well as those with positive definite metric. It enables us to construct the wavefunctional formalism of the quantum electromagnetic field equivalent to the operator formalism in covariant gauges. The theoretical foundation of the Wick rotation of the dynamical variable A0(x) is established.

High-Temperature Expansion of the Free Energy in the Two-Dimensional XY Model

We extend the high-temperature series of the free energy for the XY model in two dimensions to order β 48 from the previous order of β 22 by applying an improved algorithm of the finite lattice method. The long series obtained allows us to conclude that the behavior of the free energy is consistent to high accuracy with what is expected when the phase transition of the model is of the Kosterlitz-Thouless type.

Algorithm to calculate the partition function for Z (2) lattice gauge theory in four dimensions

Abstract An algorithm is shown for the calculation of the exact partition function of finite system in four-dimensional Z(2) lattice gauge theory. The partition functions to the size 2 × 2 × 2 × 1 are given. From them, zero-point distribution of the partition functions and the strong coupling expansion of the free energy to the order of u 24 are shown.