Phase transition for loop representations of Quantum spin systems on trees

Abstract

We consider a model of random loops on Galton-Watson trees with an offspring distribution with high expectation. We give the configurations a weighting of ${\theta }^{\#\text{loops}}$. For many $\theta >1$ these models are equivalent to certain quantum spin systems for various choices of the system parameters. We find conditions on the offspring distribution that guarantee the occurrence of a phase transition from finite to infinite loops for the Galton-Watson tree.

arXiv comment16 pages, 1 figure

References in corpus (6)

• Geometric Aspects of Quantum Spin States
• Random loop representations for quantum spin systems
• Infinite cycles in the random stirring model on trees
• Critical parameter of random loop model on trees
• Critical temperature of Heisenberg models on regular trees, via random loops
• Correlation inequalities for the quantum XY model

Cited by in corpus (4)

• The interchange process with reversals on the complete graph
• Critical temperature of Heisenberg models on regular trees, via random loops
• Critical Parameters for Loop and Bernoulli Percolation
• On a class of orthogonal-invariant quantum spin systems on the complete graph