Monte Carlo simulation of model spin systems

Wolfhard Janke E

Robert Achleitner

This thesis work deals with Monte Carlo (MC) simulations with the focus on quantum mechanical systems. I start with an introduction about Monte-Carlo methods in general and their application to the classical Ising model. The second, most important part deals with the problem in quantum mechanics, and presents a possible simulation method, the Stochastic Series Expansion (SSE). I give an introduction about the idea behind that method and give some results obtained for simulations for finite spin chains. All programming was performed in FORTRAN.

Shigeo Homma, H. Matsuda, N. Ogita

A Simple Monte Carlo simulation is proposed, which we call decoupled cell method, for equilibrium states of quantum spin systems. In one-dimensional XY-model, the result of this simulation is found to give a good approximation for the internal energy at any temperature. A discussion is given of a possibile range of applicability of this method.

Sakaguchi Toshifumi

俊文 坂口

William J. Shugard, John D. Weeks, George H. Gilmer

The results of a Monte Carlo (MC) simulation of the planar ($\mathrm{XY}$) model in the dual "solid-on-solid" representation are reported. Our estimate for the reduced transition temperature ${T}_{c}$ of 0.90 and our finding of a rather sharp peak in the specific heat about 18% above ${T}_{c}$ are in good agreement with recent MC calculations in the spin representation.