The Finite-Size Scaling Study of Five-Dimensional Ising Model

Abstract

The five-dimensional ferromagnetic Ising model is simulated on the Creutz cellular automaton algorithm using finite-size lattices with linear dimension 4 ≤ L ≤ 8. The critical temperature value of infinite lattice is found to be T χ (∞) = 8.7811 (1) using 4 ≤ L ≤ 8 which is also in very good agreement with the precise result. The value of the field critical exponent (δ = 3.0067 (2)) is good agreement with δ = 3 which is obtained from scaling law of Widom. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 2.5080 (1), 2.5005 (3) and 1.2501 (1) using 4 ≤ L ≤ 8, respectively, which are in very good agreement with the theoretical predictions of . The finite-size scaling plots of magnetic susceptibility and the order parameter verify the finite-size scaling relations about the infinitelattice temperature.

The Test of a New Critical Exponent Ϙ by Using Ising Model on the Creutz Cellular Automaton

“…Its value may be "0" or "1". The Ising spin energy, or internal energy of the lattice, H I , is given (in units of the nearest neighbor coupling constant J) by [2,3,10,11]:…”

“…In higher dimension and/or higher lattice size, the simulation of the Ising model by the conventional Monte Carlo method becomes impractical and the algorithms need to be faster. The Creutz cellular automaton [2,3] does not require high-quality random numbers, it is an order of magnitude faster than the conventional Monte Carlo method and compared to the Q2R cellular automaton [4], it has the advantage of fluctuating internal energy from which the specific heat can be computed.…”