Nonequilibrium dynamics of urn models

Dynamical urn models, such as the Ehrenfest model, played an important role in the early days of statistical mechanics. Dynamical many-urn models generalize the former models in two respects: the number of urns is macroscopic, and thermal effects are included. These many-urn models are exactly solvable in the mean-field geometry. They allow analytical investigations of the characteristic features of nonequilibrium dynamics referred to as aging, including the scaling of correlation and response functions in the two-time plane and the violation of the fluctuation-dissipation theorem. This paper contains a general presentation of these models, as well as a more detailed description of two dynamical urn models, the backgammon model and the zeta urn model.

[1]  M. Kac.  Random Walk and the Theory of Brownian Motion , 1947 .

[2]  J. Kurchan,et al.  On the out-of-equilibrium relaxation of the Sherrington-Kirkpatrick model , 1993, cond-mat/9311016.

[3]  CORRELATION AND RESPONSE IN THE BACKGAMMON MODEL : THE EHRENFEST LEGACY , 1999, cond-mat/9907259.

[4]  Ritort.  Glassiness in a Model without Energy Barriers. , 1995, Physical review letters.

[5]  Non-equilibrium dynamics of a simple stochastic model , 1997, cond-mat/9707052.

[6]  A. Bray.  Theory of phase-ordering kinetics , 1994, cond-mat/9501089.

[7]  A. Lipowski.  Absorption time in certain urn models , 1997 .

[8]  J. M. Luck,et al.  Nonequilibrium critical dynamics of ferromagnetic spin systems , 2002 .

[9]  Nonequilibrium dynamics of the zeta urn model , 2001 .

[10]  Relaxational processes and entropic traps in the Backgammon model , 1996, cond-mat/9609271.

[11]  J. Luck,et al.  Long-time regime and scaling of correlations in a simple model with glassy behaviour , 1996 .

[12]  PHASE DIAGRAM OF THE MEAN FIELD MODEL OF SIMPLICIAL GRAVITY , 1998, gr-qc/9808011.

[13]  Off equilibrium dynamics and aging in unfrustrated systems , 1994, cond-mat/9406053.

[14]  A. Siegert.  On the Approach to Statistical Equilibrium , 1949 .

[15]  Response function of coarsening systems , 1999, cond-mat/9903091.

[16]  A. Young,et al.  Spin glasses and random fields , 1997 .

[17]  Jean-Philippe Bouchaud,et al.  Slow dynamics and aging in spin glasses , 1996, cond-mat/9607224.

[18]  Response of non-equilibrium systems at criticality: ferromagnetic models in dimension two and above , 2000, cond-mat/0001264.

[19]  Huse.  Remanent magnetization decay at the spin-glass critical point: A new dynamic critical exponent for nonequilibrium autocorrelations. , 1989, Physical review. B, Condensed matter.

[20]  F. G. Hess.  Alternative Solution to the Ehrenfest Problem , 1954 .

[21]  A. Barrat.  MONTE CARLO SIMULATIONS OF THE VIOLATION OF THE FLUCTUATION-DISSIPATION THEOREM IN DOMAIN GROWTH PROCESSES , 1998 .

[22]  Z. Burda,et al.  Condensation in the Backgammon model , 1997 .

[23]  Relaxation at late stages in an entropy barrier model for glassy systems , 1997 .

[24]  DYNAMICAL SOLUTION OF A MODEL WITHOUT ENERGY BARRIERS , 1995, cond-mat/9505115.

[25]  LETTER TO THE EDITOR: A simple stochastic model for the dynamics of condensation , 1997, cond-mat/9708010.

[26]  Jean-Philippe Bouchaud,et al.  Entropy barriers and slow relaxation in some random walk models , 1995 .

[27]  ENERGY FLOW, PARTIAL EQUILIBRATION, AND EFFECTIVE TEMPERATURES IN SYSTEMS WITH SLOW DYNAMICS , 1997, cond-mat/9611044.

[28]  H. Janssen,et al.  New universal short-time scaling behaviour of critical relaxation processes , 1989 .

[29]  Response of non-equilibrium systems at criticality: exact results for the Glauber-Ising chain , 1999, cond-mat/9911348.

[30]  Z. Burda,et al.  Finite size scaling of the balls in boxes model , 2000 .

[31]  S. Franz,et al.  Glassy mean-field dynamics of the backgammon model , 1996 .