Sharp phase transition in the random stirring model on trees

DOI10.1007/s00440-013-0543-7zbMath1317.60130arXiv1202.1322OpenAlexW2124324912MaRDI QIDQ2343023

Alan Hammond

Publication date: 4 May 2015

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1322

zbMATH Keywords

phase transitioncritical timeregular treesrandom permutationsrandom stirring model

Mathematics Subject Classification ID

Trees (05C05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Critical phenomena in equilibrium statistical mechanics (82B27)

Related Items (max. 100)

Critical parameter of random loop model on trees ⋮ The free energy in a class of quantum spin systems and interchange processes ⋮ Critical Parameters for Loop and Bernoulli Percolation ⋮ Phase transition for loop representations of quantum spin systems on trees ⋮ The probability of long cycles in interchange processes ⋮ Limit distributions for Euclidean random permutations ⋮ The interchange process on high-dimensional products ⋮ On the cycle structure of Mallows permutations ⋮ Random loop representations for quantum spin systems ⋮ Critical temperature of Heisenberg models on regular trees, via random loops ⋮ The interchange process with reversals on the complete graph ⋮ Phase transition for the interchange and quantum Heisenberg models on the Hamming graph ⋮ Existence of a phase transition of the interchange process on the Hamming graph ⋮ Sharp phase transition for random loop models on trees ⋮ The mean-field quantum Heisenberg ferromagnet via representation theory ⋮ Critical point for infinite cycles in a random loop model on trees

Cites Work

• Unnamed Item
• The probability of long cycles in interchange processes
• Emergence of giant cycles and slowdown transition in random transpositions and \(k\)-cycles
• Random trees and applications
• Improved lower bound on thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet
• Compositions of random transpositions
• Nearest-neighbor Markov interaction processes on multidimensional lattices
• Quantum Heisenberg models and their probabilistic representations
• Proof of Aldous’ spectral gap conjecture
• Percolation
• Atomic Theory of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi></mml:math>Transition in Helium

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