Generalised Bose-Einstein phase transition in large-$m$ component spin glasses

Abstract

It is proposed to understand finite dimensional spin glasses using a $1/m$ expansion, where $m$ is the number of spin components. It is shown that this approach predicts a replica symmetric state in finite dimensions. The point about which the expansion is made, the infinite-$m$ limit, has been studied in the mean-field limit in detail and has a very unusual phase transition, rather similar to a Bose-Einstein phase transition but with $N^{2/5}$ macroscopically occupied low-lying states.

4 pages (plus a few lines), 3 figures. v2: minor error corrected. v3: numerics supplemented by analytical arguments, references added, figure of density of states added

References in corpus (5)

• Single spin- and chiral-glass transition in vector spin glasses in three-dimensions
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• Chiral-glass transition and replica symmetry breaking of a three-dimensional Heisenberg spin glass
• Ordering of the Heisenberg Spin Glass in High Dimensions
• Ground State and Spin Glass Phase of the Large N Infinite Range Spin Glass Via Supersymmetry

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• Approximating the XY model on a random graph with a $q$-state clock model
• One-dimensional infinite component vector spin glass with long-range interactions
• Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
• The 1/m expansion in spin glasses and the de Almeida-Thouless line
• Random Coulomb antiferromagnets: from diluted spin liquids to Euclidean random matrices
• Spin glasses in the limit of an infinite number of spin components
• Bose-Einstein-Like condensation of deformed random matrix: A replica approach
• Defect energy of infinite-component vector spin glasses
• Inherent Structures in m-component Spin Glasses
• Dependence of ground state energy of classical n-vector spins on n
• The m-component spin glass on a Bethe lattice
• Sample-to-sample fluctuations and bond chaos in the $m$-component spin glass