On cluster properties of classical ferromagnets in an external magnetic field

Abstract

Correlation functions of ferromagnetic spin systems satisfying a Lee-Yang property are studied. It is shown that, for classical systems in a non-vanishing uniform external magnetic field $h$, the connected correlation functions decay exponentially in the distances between the spins, i.e., the inverse correlation length ("mass gap"), $m(h)$, is strictly positive. Our proof is very short and transparent and is valid for complex values of the external magnetic field $h$, provided that $\text{Re}h\ne 0$. It implies a mean-field lower bound on $m(h)$, as $h\searrow 0$, first established by Lebowitz and Penrose for the Ising model. Our arguments also apply to some quantum spin systems.

12 pages

References in corpus (1)

• Some Applications of the Lee-Yang Theorem

Cited by in corpus (2)

• The Strong Gauss Lucas Theorem and Analyticity of Correlation Functions via the Lee-Yang Theorem
• Phase Transitions, Spontaneous Symmetry Breaking, and Goldstone's Theorem