The Ising Model on the Random Planar Causal Triangulation: Bounds on the Critical Line and Magnetization Properties

TY - JOUR

T1 - The Ising Model on the Random Planar Causal Triangulation

T2 - Bounds on the Critical Line and Magnetization Properties

AU - Napolitano, George M.

AU - Turova, Tatyana S.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - We investigate a Gibbs (annealed) probability measure defined on Ising spin configurations on causal triangulations of the plane. We study the region where such measure can be defined and provide bounds on the boundary of this region (critical line). We prove that for any finite random triangulation the magnetization of the central spin is sensitive to the boundary conditions. Furthermore, we show that in the infinite volume limit, the magnetization of the central spin vanishes for values of the temperature high enough.

AB - We investigate a Gibbs (annealed) probability measure defined on Ising spin configurations on causal triangulations of the plane. We study the region where such measure can be defined and provide bounds on the boundary of this region (critical line). We prove that for any finite random triangulation the magnetization of the central spin is sensitive to the boundary conditions. Furthermore, we show that in the infinite volume limit, the magnetization of the central spin vanishes for values of the temperature high enough.

KW - Gibbs measure

KW - Ising model

KW - Random graphs

U2 - 10.1007/s10955-015-1430-7

DO - 10.1007/s10955-015-1430-7

M3 - Journal article

AN - SCOPUS:84955448710

SN - 0022-4715

VL - 162

SP - 739

EP - 760

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3

ER -