Thursday, 17 December, 2015

## Published in:

arXiv:1512.05707

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 \not= 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.