Gauge symmetries in random magnetic systems

1978/11/01 by Eduardo Fradkin, Bernardo A. Huberman, Stephen H. Shenker · 6 citations
Physics and Astronomy · #Theoretical and Computational Physics #Quantum many-body systems #Quantum Chromodynamics and Particle Interactions

paper · doi:10.1103/physrevb.18.4789

openalex publication_date 1978/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

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.

Citations

• Solvable spin systems with random interactions
• Ordering, metastability and phase transitions in two-dimensional systems
• Order and disorder in gauge systems and magnets
• Hamiltonian formulation of Wilson's lattice gauge theories

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• Search for a vortex loop blowout transition in a type-II superconductor in a finite magnetic field
• Regularization and decimation pseudolikelihood approaches to statistical inference inXYspin models
• The uniformly frustrated two-dimensionalXYmodel in the limit of weak frustration
• Frustration in Vicinity of Transition Point of Ising Spin Glasses
• Critical exponents of the fully frustrated two-dimensionalXYmodel
• Quantum chromodynamics [wikipedia]