Article

# Correlations in avalanche critical points.

Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia.

Physical Review E (Impact Factor: 2.31). 08/2009; 80(1 Pt 1):011105. DOI: 10.1103/PhysRevE.80.011105 Source: PubMed

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**ABSTRACT:**We review some results for the dynamics of first-order phase transitions in functional materials. We especially focus on simple models of athermal evolution in driven ferromagnets that give a global picture of metastability and hysteresis, showing that first-order phase transitions in such systems proceed by avalanches. Within this theoretical framework, we then discuss recent experiments on acoustic emission avalanches in structural phase transitions. Comment: 24 pages, 11 figures, intended as a chapter in book "Disorder and Strain induced complexity in functional materials" (This version includes the missing figures)09/2010; - [Show abstract] [Hide abstract]

**ABSTRACT:**Hysteretic systems may exhibit a runaway avalanche in which a large fraction of the constituents of the system collectively change state. It would be very valuable to understand the role that interaction strength between constituents plays in the size of such catastrophic runaway avalanches. We use a simple model, the random field Ising model, to study how the size of the runaway avalanche changes as the coupling between spins, J, is tuned. In particular, we calculate P(S), the distribution of size changes S in the runaway avalanche size as J comes close to a critical value J(c), and find that the distribution scales as P(S)∼S(-τ)D(S(σ)(J/J(c)-1)), with τ and σ critical exponents and D(x) a universal scaling function. In mean field theory we find τ=3/2, σ=1/2, and D(x)=exp[-(3x)(1/σ)/2]. On the basis of these results and previous studies, we also predict that for three dimensions τ=1.6 and σ=0.24.Physical Review E 10/2011; 84(4 Pt 1):041129. · 2.31 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.Physical Review E 02/2013; 87(2-1):022121. · 2.31 Impact Factor

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