Motion of Lee-Yang zeros

Abstract

We consider the zeros of the partition function of the Ising model with ferromagnetic pair interactions and complex external field. Under the assumption that the graph with strictly positive interactions is connected, we vary the interaction (denoted by $t$) at a fixed edge. It is already known that each zero is monotonic (either increasing or decreasing) in $t$; we prove that its motion is local: the entire trajectories of any two distinct zeros are disjoint. If the underlying graph is a complete graph and all interactions take the same value $t\ge 0$ (i.e., the Curie-Weiss model), we prove that all the principal zeros (those in $i[0,\pi /2)$) decrease strictly in $t$.

arXiv comment16 pages, 1 figure

References in corpus (7)

• Observation of Lee-Yang zeros
• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Partition function zeros at first-order phase transitions: A general analysis
• Partition function zeros at first-order phase transitions: Pirogov-Sinai theory
• Limiting Measure of Lee--Yang Zeros for the Cayley Tree
• Ising model with Curie-Weiss perturbation
• Monotonicity of Ursell functions in the Ising model

Cited by in corpus (2)

• Monotonicity of Ursell functions in the Ising model
• Lee-Yang zeros and quantum Fisher information matrix in a nonlinear system