The mean-field quantum Heisenberg ferromagnet via representation theory

DOI10.1214/20-AIHP1067MaRDI QIDQ2077318

Gil Alon, Gady Kozma

Publication date: 25 February 2022

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.10530

zbMATH Keywords

phase transitionsymmetric grouprandom walkinterchange processmagnetisationquantum heizenberg ferromagnet

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Interacting particle systems in time-dependent statistical mechanics (82C22) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (2)

Quantum spins and random loops on the complete graph ⋮ Heisenberg models and Schur-Weyl duality

Cites Work

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• The random interchange process on the hypercube
• The probability of long cycles in interchange processes
• Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case
• Interaction of Markov processes
• Random walk representations of the Heisenberg model
• Comparison techniques for random walk on finite groups
• The Kronecker product of Schur functions indexed by two-row shapes or hook shapes
• Comparing with octopi
• Phase transition for the interchange and quantum Heisenberg models on the Hamming graph
• Sharp phase transition in the random stirring model on trees
• Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet
• Improved lower bound on thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet
• Compositions of random transpositions
• A phase transition in the random transposition random walk
• Large cycles in random permutations related to the Heisenberg model
• Counterexamples to ferromagnetic ordering of energy levels
• The free energy in a class of quantum spin systems and interchange processes
• Generating a random permutation with random transpositions
• Cycle structure of the interchange process and representation theory
• Infinite cycles in the random stirring model on trees

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