Numerical Studies of Phase Transitions in Disorderd Systems

University Of California-Santa Cruz, Santa Cruz CA

Investigators

Abstract

0086287 Young This grant supports theoretical research on phase transitions in disordered systems. The work is primarily numerical. The research will focus on two areas. The first is to investigate the nature of the spin glass state, which occurs in systems with frustration and disorder. Although the terminology refers to a class of magnetic systems, the concepts developed in spin glasses have a much wider applicability and have found use in other areas of science such as protein folding and optimization problems. Only limited results have been obtained analytically, so numerical simulations have played an important role. Past work has established fairly conclusively that a finite temperature transition does occur. The nature of the spin glass state below the transition temperature is, however, fairly controversial. Recently the PI's group has embarked on a series of studies to elucidate the nature of the spin glass state by investigating how the ground state changes when various types of perturbations are applied. Because of frustration, determination of the ground state is non-trivial and required a fairly sophisticated genetic algorithm. These calculations suggest a picture of the spin glass which is a modified version of one of the proposed theories, the droplet picture, but also contains an important ingredient of the alternative theory, replica symmetry breaking. During the course of this grant, the PI will investigate this scenario in more detail, and, most importantly, check that it is also consistent with finite temperature Monte Carlo simulations on rather small sizes but taken down to temperatures much lower than before using the exchange Monte Carlo method, which considerably reduces the slowing down that occurs at low temperature in conventional Monte Carlo. Since numerical results on spin glasses can only be done on rather small systems at low temperatures, because of long relaxation times due to the many-valley nature of the phase space (which is only partially reduced by the exchange Monte Carlo method), a major concern in the interpretation of numerical data is the size of the corrections to scaling. The PI therefore also intends to look systematically at how the size of these corrections varies for different models, to see if there is an optimal model for which the corrections are smallest. Finally, the second area that will be studied concerns quantum phase transitions with disorder. These are poorly understood compared with classical phase transitions at finite temperature. This is because many of the techniques used successfully in classical transitions don't work in the quantum case, perhaps because non-perturbative (Griffiths-McCoy) effects are important. Hence again, numerical work has been very important. Several studies will be carried out. %%% This grant supports theoretical research on phase transitions in disordered systems. The work is primarily numerical. The research will focus on two areas. The first is to investigate the nature of the spin glass state, which occurs in systems with frustration and disorder. Although the terminology refers to a class of magnetic systems, the concepts developed in spin glasses have a much wider applicability and have found use in other areas of science such as protein folding and optimization problems. Only limited results have been obtained analytically, so numerical simulations have played an important role. The second area that will be studied concerns quantum phase transitions with disorder. These are poorly understood compared with classical phase transitions at finite temperature. This is because many of the techniques used successfully in classical transitions don't work in the quantum case, perhaps because non-perturbative (Griffiths-McCoy) effects are important. Hence again, numerical work has been very important. Several studies will be carried out. ***