Thermodynamics of histories for the one-dimensional contact process
| Autor: | Carlo Vanderzande, Jef Hooyberghs |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
Physics Phase transition Contact process Statistical Mechanics (cond-mat.stat-mech) Stochastic process Density matrix renormalization group FOS: Physical sciences Thermodynamics Statistical and Nonlinear Physics Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Critical value density matrix renormalization group calculations phase transitions into absorbing states (theory) fluctuations (theory) stochastic processes (theory) Statistics Probability and Uncertainty Critical exponent Scaling Condensed Matter - Statistical Mechanics Phase diagram |
| Popis: | The dynamical activity K(t) of a stochastic process is the number of times it changes configuration up to time t. It was recently argued that (spin) glasses are at a first order dynamical transition where histories of low and high activity coexist. We study this transition in the one-dimensional contact process by weighting its histories by exp(sK(t)). We determine the phase diagram and the critical exponents of this model using a recently developed approach to the thermodynamics of histories that is based on the density matrix renormalisation group. We find that for every value of the infection rate, there is a phase transition at a critical value of s. Near the absorbing state phase transition of the contact process, the generating function of the activity shows a scaling behavior similar to that of the free energy in an equilibrium system near criticality. 16 pages, 7 figures |
| Databáze: | OpenAIRE |
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