Sharp phase transition for random loop models on trees

DOI10.1214/21-EJP677zbMath1491.60171arXiv1812.03937MaRDI QIDQ2076607

Volker Betz, Benjamin Lees, Lukas Roth, Johannes Ehlert

Publication date: 22 February 2022

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.03937

zbMATH Keywords

phase transitionrandom interchangerandom stirringrandom loop model

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Emergence of giant cycles and slowdown transition in random transpositions and \(k\)-cycles
• Geometric aspects of quantum spin states
• Critical parameter of random loop model on trees
• Critical temperature of Heisenberg models on regular trees, via random loops
• Phase transition for the interchange and quantum Heisenberg models on the Hamming graph
• Quantum spins and random loops on the complete graph
• The interchange process with reversals on the complete graph
• Existence of a phase transition of the interchange process on the Hamming graph
• Critical point for infinite cycles in a random loop model on trees
• Sharp phase transition in the random stirring model on trees
• Improved lower bound on thermodynamic pressure of the spin 1/2 Heisenberg ferromagnet
• Compositions of random transpositions
• Large cycles in random permutations related to the Heisenberg model
• Nearest-neighbor Markov interaction processes on multidimensional lattices
• A numerical study of the 3D random interchange and random loop models
• Phase transition for loop representations of quantum spin systems on trees
• A Multivariate Faa di Bruno Formula with Applications
• Cycle structure of the interchange process and representation theory
• Random loop representations for quantum spin systems
• Infinite cycles in the random stirring model on trees
• Critical Parameters for Loop and Bernoulli Percolation

This page was built for publication: Sharp phase transition for random loop models on trees