Curie Temperature for Small World Ising Systems of Different Dimensions
E.Z. Meilikhov, and R.M. Farzetdinova
TL;DR
This paper derives how the Curie temperature in Small World Ising systems varies with the fraction of long-range links across different dimensions, revealing specific mathematical dependencies.
Contribution
It introduces dimension-specific formulas for the Curie temperature dependence on long-range link concentration in Small World Ising models.
Findings
T_C(p) ~ 1/ln|p| for 1D systems
T_C(p) ~ p^{1/2} for 2D systems
T_C(p) ~ p^{2/3} for 3D systems
Abstract
For Small World Ising systems of different dimensions, "concentration" dependencies T_C(p) of the Curie temperature upon the fraction p of long-range links have been derived on a basis of simple physical considerations. We have found T_C(p) ~ 1/ln|p| for 1D, T_C(p) ~ p^{1/2} for 2D, and T_C(p) ~ p^{2/3} for 3D.
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