Strongly coupled systems : from quantum antiferromagnets to unified models for superconductors

Abstract

I discuss the significance of the antiferromagnetic Heisenberg model (AFHM) in both high-energy and condensed-matter physics, and proceed to describe an efficient cluster algorithm used to simulate the AFHM. This is one of two algorithms with which my collaborators and I were able to obtain numerical results that definitively confirm that chiral perturbation theory, corrected for cutoff effects in the AFHM, leads to a correct field-theoretical description of the low-temperature behavior of the spin correlation length in various spin representations S. Using a finite-size-scaling technique, we explored correlation lengths of up to 105 lattice spacings for spins S=1 and 5/2. We show how the recent prediction of cutoff effects by P. Hasenfratz is approached for moderate correlation lengths, and smoothly connects with other approaches to modeling the AFHM at smaller correlation lengths. I also simulate and discuss classical antiferromagnetic systems with simultaneous SO(M) and SO(N) symmetries, which have been proposed as models for magnets in external fields and for electronic and color superconductors. After detailing the algorithms which were employed, I present results for the various observables which confirm the existence of the expected ordered and disordered phases. I obtain a preliminary phase diagram from these systems, from which the location of an expected bicritical point may be estimated. This is a necessary first step in determining whether the point exhibits a dynamically-generated enhanced symmetry, a possibility first suggested by Wiese and Chandrasekharan but not fully resolved in three dimensions.