Nonmonotonic external field dependence of the magnetization in a finite Ising model: Theory and MC simulation

X. S. Chen; V. Dohm; D. Stauffer

doi:10.1007/s100510051081

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Nonmonotonic external field dependence of the magnetization in a finite Ising model: Theory and MC simulation

X. S. Chen¹^,2, V. Dohm² and D. Stauffer³

¹ Institute of Particle Physics, Hua-Zhong Normal University, Wuhan 430079, P.R. China
² Institut für Theoretische Physik, Technische Hochschule Aachen, 52056 Aachen, Germany
³ Institute for Theoretical Physics, Cologne University, 50923 Köln, Germany

Received: 20 July 1999
Revised: 11 November 1999
Published online: 15 April 2000

Abstract

Using $\varphi^4$ field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization M for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory with infinite cutoff gives a scaling form of the equation of state $h/M^\delta = f(hL^{\beta\delta/\nu}, t/h^{1/\beta\delta})$ where $t=(T-T_{\rm c})/T_{\rm c}$ is the reduced temperature, h is the external field and L is the size of system. Below T_c and at T_c the theory predicts a nonmonotonic dependence of f(x,y) with respect to $x \equiv hL^{\beta\delta/\nu}$ at fixed $y \equiv t/h^{1/\beta \delta}$ and a crossover from nonmonotonic to monotonic behaviour when y is further increased. These results are confirmed by MC simulation. The scaling function f(x,y) obtained from the field theory is in good quantitative agreement with the finite-size MC data. Good agreement is also found for the bulk value $f(\infty,0)$ at T_c.

PACS: 05.70.Jk – Critical point phenomena / 64.60.-i – General studies of phase transitions

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Nonmonotonic external field dependence of the magnetization in a finite Ising model: Theory and MC simulation

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