Dynamical barriers for the random ferromagnetic Ising model on the Cayley tree : traveling-wave solution of the real space renormalization flow - Archive ouverte HAL Access content directly
Journal Articles Journal of Statistical Mechanics Year : 2013

## Dynamical barriers for the random ferromagnetic Ising model on the Cayley tree : traveling-wave solution of the real space renormalization flow

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Cécile Monthus

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Thomas Garel
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#### Abstract

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.

#### Domains

Physics [physics]

### Dates and versions

cea-01323467 , version 1 (30-05-2016)

### Identifiers

• HAL Id : cea-01323467 , version 1
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### Cite

Cécile Monthus, Thomas Garel. Dynamical barriers for the random ferromagnetic Ising model on the Cayley tree : traveling-wave solution of the real space renormalization flow. Journal of Statistical Mechanics, 2013, 2013 (5), pp.5012. ⟨10.1088/1742-5468/2013/05/P05012⟩. ⟨cea-01323467⟩

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