Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Apr;79(4):041138. doi: 10.1103/PhysRevE.79.041138. Epub 2009 Apr 23.

Effects of discreteness on gauge glass models in two and three dimensions.

Physical review. E, Statistical, nonlinear, and soft matter physics

Satoshi Yotsuyanagi, Yusuke Suemitsu, Yukiyasu Ozeki

PMID: 19518204 DOI: 10.1103/PhysRevE.79.041138

Abstract

The q-state clock gauge glass model is studied to see the effect of discreteness on the Kosterlitz-Thouless (KT) transition and the ferromagnetic (FM) critical phenomenon in random systems. The nonequilibrium relaxation analysis is applied. In two dimensions, the successive transitions of paramagnetic (PM), KT, and FM phases are investigated along the Nishimori line for q=6, 8, 10, 12, 14, 16, and 1024 (recognized as infinity) cases. For the upper critical temperature, it is found that the transition temperature is almost the same as in the continuous case for all q values. The lower transition temperature is found to be proportional to 1/q2. In three dimensions, the critical behavior of the PM-FM transition is studied along the Nishimori line for q=6, 8, 16, and 1024 cases. It is found that the spin discreteness is irrelevant, and the transition belongs to the same universality class as in the (continuous) XY case.

Publication Types

• Journal Article
• Research Support, Non-U.S. Gov't