Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-07-21
Physics
Condensed Matter
Statistical Mechanics
LaTex, 12 pages
Scientific paper
10.1007/s100510051081
Using $\phi^4$ 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 $t=(T-T_c)/T_c$ 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 $T_c$.
Chen Xiang-Song
Dohm Volker
Stauffer Dietrich
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