arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1601.05643cond-mat.dis-nn
收藏

Dyson长程铁磁和自旋玻璃模型有限温度下静动力学的实空间重整化

Real-space renormalization for the finite temperature statics and dynamics of the Dyson Long-Ranged Ferromagnetic and Spin-Glass models

Cecile Monthus

备注：
14 pages, 2 figures
发表信息：
J. Stat. Mech. (2016) 043302
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

利用实空间重正化规则研究了Dyson分级经典自旋模型的有限温度动力学。对于包含长程耦合$J(r) \propto r^{-1-σ}$的铁磁模型，在$1/2<σ<1$中存在非平均场的热铁磁-顺磁相变，求解了RG流：特征弛豫时间$τ(L)$在相变时遵循临界幂律$τ(L)\propto L^{z_c(σ)} $，在铁磁相中遵循激活律$\ln τ(L)\propto L^ψ $和$ψ=1-σ$.对于在存在非平均场的热自旋玻璃-顺磁跃迁的区域$2/3<σ<1$中包含变化$\overline{J^2(r)} \propto r^{-2σ}$的随机长程耦合的自旋玻璃模型，数值研究了耦合和弛豫时间的耦合RG流：弛豫时间$τ(L)$在临界态服从幂律$τ(L)\propto L^{z_c(σ)} $，在自旋态服从激活律$\ln τ(L)\propto L^ψ $。玻璃相，其动力学指数$ψ=1-σ=θ$与控制耦合$J(L) \propto L^θ $流动的液滴指数一致。

英文摘要：

The finite temperature dynamics of the Dyson hierarchical classical spins models is studied via real-space renormalization rules concerning the couplings and the relaxation times. For the ferromagnetic model involving Long-Ranged coupling $J(r) \propto r^{-1-σ}$ in the region $1/2<σ<1$ where there exists a non-mean-field-like thermal Ferromagnetic-Paramagnetic transition, the RG flows are explicitly solved: the characteristic relaxation time $τ(L)$ follows the critical power-law $τ(L)\propto L^{z_c(σ)} $ at the phase transition and the activated law $\ln τ(L)\propto L^ψ $ with $ψ=1-σ$ in the ferromagnetic phase. For the Spin-Glass model involving random Long-Ranged couplings of variance $\overline{J^2(r)} \propto r^{-2σ}$ in the region $2/3<σ<1$ where there exists a non-mean-field-like thermal SpinGlass-Paramagnetic transition, the coupled RG flows of the couplings and of the relaxation times are studied numerically : the relaxation time $τ(L)$ follows some power-law $τ(L)\propto L^{z_c(σ)} $ at criticality and the activated law $\ln τ(L)\propto L^ψ $ in the Spin-Glass phase with the dynamical exponent $ψ=1-σ=θ$ coinciding with the droplet exponent governing the flow of the couplings $J(L) \propto L^θ $.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑