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Gauge symmetries in random magnetic systems

1978; American Physical Society; Volume: 18; Issue: 9 Linguagem: Inglês

10.1103/physrevb.18.4789

1095-3795

Eduardo Fradkin, Bernardo A. Huberman, Stephen H. Shenker,

Quantum Chromodynamics and Particle Interactions

We study random magnetic systems emphasizing the concept of gauge invariance and gauge-invariant disorder (frustration) introduced by Toulouse and Anderson. We formulate our models in a gauge-invariant manner and introduce gauge-invariant correlation functions to isolate the effects of gauge-invariant disorder. Specifically, we study the Ising and $X\ensuremath{-}Y$ models in two and three dimensions in a frozen distribution of frustrations. Using duality transformations, we obtain expressions for the energetics of frustrations and their effect on correlations. We study simple configurations of frustrations quantitatively. In addition we reformulate the quenching procedure in terms of frustrations.