Cayley树上随机铁磁伊辛模型的动力学势垒：实空间重整化流的行波解
Dynamical barriers for the random ferromagnetic Ising model on the Cayley tree : traveling-wave solution of the real space renormalization flow
摘要：
研究了分支比为$K$的Cayley树上随机铁磁伊辛模型在零温附近的随机动力学.我们应用边界实空间重整化过程中介绍了我们以前的工作（C。Monthus和T. Garel，J. Stat. Mech.P02037（2013）），以便导出动力学势垒的重正化规则。得到了$n$代数子树的动力学势垒概率分布$P_n(B)$对于大$n$收敛于某个行波$P_n(B) \simeq P^*(B-nv) $，即概率分布的宽度在一个平均值附近保持有限，该平均值随代数$n$线性增长.我们提出了分支比K=2和K=3的数值结果。我们还计算了K=2时速度$v$的弱无序展开。
英文摘要：
We consider the stochastic dynamics near zero-temperature of the random ferromagnetic Ising model on a Cayley tree of branching ratio $K$. We apply the Boundary Real Space Renormalization procedure introduced in our previous work (C. Monthus and T. Garel, J. Stat. Mech. P02037 (2013)) in order to derive the renormalization rule for dynamical barriers. We obtain that the probability distribution $P_n(B)$ of dynamical barrier for a subtree of $n$ generations converges for large $n$ towards some traveling-wave $P_n(B) \simeq P^*(B-nv) $, i.e. the width of the probability distribution remains finite around an average-value that grows linearly with the number $n$ of generations. We present numerical results for the branching ratios K=2 and K=3. We also compute the weak-disorder expansion of the velocity $v$ for K=2.
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