Finite-Size Scaling Study of the Simple Cubic Three-State Potts Glass

Abstract

During the last few years the Potts glass model has attracted more and more attention. It is considered as a first step towards modelling the phase transition of structural and orientational glasses. A mean-field approach /1/ predicts a low temperature behavior completely different from what is known from Ising spin glasses /2/. But short range models differ markedly from mean-field-predictions. So it is natural to ask, how the short range Potts glass behaves. Especially the question of the lower critical dimension d _l is important, below which a finite temperature transition ceases to occur. We tried to answer this by combining Monte-Carlo simulations with a finite-size scaling analysis. The model is defined by the following Hamiltonian

$$H = - \sum\limits_{ < i,j > } {{J_{ij}}} {\delta _{ni,nj}}\,;\,{n_i}\, \in \{ 1,2, \cdots ,p\} $$

where the sum is over all nearest neighbor pairs of the simple cubic lattice. The couplings are Gaussian with zero mean and variance one, which merely sets the temperature scale. We further restrict to p = 3.