Rigorous results on ferromagnetic lattice spin systems. I

Abstract

The Lee–Yang theorem was extended to the case of the correlation functions of the Ising ferromagnets (s=1/2). Each adjacent pair of zeros of the (n+1)th correlation function in the complex fugacity plane is separated by one and only one zero of the nth correlation function (n=0,1,2,...,N−1), and none of zeros of each function degenerate except for the infinite temperature in the completely connected system. The first Griffiths’ inequality for the correlation function was elaborated such as 〈σ1σ2⋅⋅⋅σn〉⩽ tanhn(mh/kT). The inequality for the free energy in the presence of the external field was obtained as −mh⩽ (h,T)−ℱ (0,T) ⩽−kT log[cosh(mh/kT)].