Glauber dynamics on the cycle is monotone. (English) Zbl 1068.82014

Nacu, Şerban

Probab. Theory Relat. Fields 127, No. 2, 177-185 (2003).

Summary: We study heat-bath Glauber dynamics for the ferromagnetic Ising model on a finite cycle (a graph where every vertex has degree two). We prove that the relaxation time \(\tau_2\) is an increasing function of any of the couplings \(J_{xy} \). We also prove some further inequalities, and obtain exact asymptotics for \(\tau_2\) at low temperatures.

MSC:

82C20	Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
60K35	Interacting random processes; statistical mechanics type models; percolation theory