Effective Potential for Scalar Field in Three Dimensions: Ising Model in the Ferromagnetic Phase

Дата и время публикации : 1996-01-29T21:30:50Z

Авторы публикации и институты :
M. M. Tsypin

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: 13 pages, 5 Postscript figures, uses epsf.sty
Первичная категория: hep-lat

Все категории : hep-lat, cond-mat, hep-ph, hep-th

Краткий обзор статьи: We compute the effective potential $V_{rm eff}(phi)$ for one-component real scalar field $phi$ in three Euclidean dimensions (3D) in the case of spontaneously broken symmetry, from the Monte Carlo simulation of the 3D Ising model in external field at temperatures approaching the phase transition from below. We study probability distributions of the order parameter on the lattices from $30^3$ to $74^3$, at $L/xi approx 10$. We find that, in close analogy with the symmetric case, $phi^6$ plays an important role: $V_{rm eff}(phi)$ is very well approximated by the sum of $phi^2$, $phi^4$ and $phi^6$ terms. An unexpected feature is the negative sign of the $phi^4$ term. As close to the continuum limit as we can get ($xi approx 7.2$), we obtain $$ {cal L}_{rm eff} approx {1 over 2} partial_mu phi partial_mu phi + 1.7 (phi^2 – eta^2)^2 (phi^2 + eta^2). $$ We also compute several universal coupling constants and ratios, including the combination of critical amplitudes $C^- (f_1^-)^{-3} B^{-2}$.

Category: Physics