Topics in coarsening phenomena

These lecture notes give a very short introduction to coarsening phenomena and summarize some recent results in the field. They focus on three aspects: the super-universality hypothesis, the geometry of growing structures, and coarsening in the spiral kinetically constrained model.

[1]  J. Cahn,et al.  A microscopic theory for antiphase boundary motion and its application to antiphase domain coasening , 1979 .

[2]  M. Picco,et al.  Geometrical properties of parafermionic spin models , 2008, 0812.3526.

[3]  A. Bray,et al.  Universality class for domain growth in random magnets , 1991 .

[4]  H. C. Andersen,et al.  Facilitated spin models, mode coupling theory, and ergodic–nonergodic transitions , 2000 .

[5]  W. Werner.  Lectures on two-dimensional critical percolation , 2007, 0710.0856.

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

[7]  D. Huse,et al.  Pinning and roughening of domain walls in Ising systems due to random impurities. , 1985, Physical review letters.

[8]  Sanjay Puri,et al.  Kinetics of Phase Transitions , 2004 .

[9]  Non-algebraic domain growth for phase ordering dynamics in a random field , 1993 .

[10]  Growing Length Scales during Aging in 2d Disordered Systems , 2004, cond-mat/0411234.

[11]  Bertrand Duplantier.  Conformal Fractal Geometry and Boundary Quantum Gravity , 2003 .

[12]  H. Stanley,et al.  Phase Transitions and Critical Phenomena , 2008 .

[13]  A. Bray,et al.  Geometric properties of two-dimensional coarsening with weak disorder , 2007, 0711.3848.

[14]  I. Lifshitz,et al.  The kinetics of precipitation from supersaturated solid solutions , 1961 .

[15]  Mauro Sellitto,et al.  Facilitated spin models on Bethe lattice: Bootstrap percolation, mode-coupling transition and glassy dynamics , 2005 .

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

[17]  H. Risken.  The Fokker-Planck equation : methods of solution and applications , 1985 .

[18]  J. Jäckle.  Models of cooperative diffusion , 2002 .

[19]  Giulio Biroli,et al.  Spiral Model: a cellular automaton with a discontinuous glass transition , 2007, 0709.0378.

[20]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[21]  Spiral model, jamming percolation and glass-jamming transitions , 2007, 0709.0583.

[22]  Cristóbal López,et al.  Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  N. Goldenfeld.  Lectures On Phase Transitions And The Renormalization Group , 1972 .

[24]  C. Fortuin,et al.  On the random-cluster model: I. Introduction and relation to other models , 1972 .

[25]  Miller,et al.  Macroscopic equilibrium from microscopic irreversibility in a chaotic coupled-map lattice. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  D. Huse,et al.  Corrections to late-stage behavior in spinodal decomposition: Lifshitz-Slyozov scaling and Monte Carlo simulations. , 1986, Physical review. B, Condensed matter.

[27]  J. P. Garrahan,et al.  Non-equilibrium dynamics of spin facilitated glass models , 2007, Journal of Statistical Mechanics: Theory and Experiment.

[28]  M. A. Muñoz,et al.  Langevin description of critical phenomena with two symmetric absorbing states. , 2004, Physical review letters.

[29]  John Cardy,et al.  Exact Results for the Universal Area Distribution of Clusters in Percolation, Ising, and Potts Models , 2002 .

[30]  C. Vanderzande,et al.  Bulk, surface and hull fractal dimension of critical Ising clusters in d=2 , 1989 .

[31]  L. Cugliandolo,et al.  Out-of-equilibrium dynamics of the spiral model , 2009, 0907.3467.

[32]  J. J. ckle.  Models of cooperative diffusion , 2002 .

[33]  J. Jäckle,et al.  Blocking transitions in lattice spin models with directed kinetic constraints , 1992 .

[34]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[35]  Jeferson J Arenzon,et al.  Curvature-driven coarsening in the two-dimensional Potts model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  U. Täuber.  Field-Theory Approaches to Nonequilibrium Dynamics , 2007 .

[37]  E. Domany,et al.  Rigorous derivation of domain growth kinetics without conservation laws , 1990 .

[38]  Daniel S Fisher,et al.  Jamming percolation and glass transitions in lattice models. , 2005, Physical review letters.

[39]  Wolfhard Janke,et al.  Geometrical vs. Fortuin–Kasteleyn clusters in the two-dimensional q-state Potts model , 2004 .

[40]  R. H. Schonmann,et al.  Lifshitz' law for the volume of a two-dimensional droplet at zero temperature , 1995 .

[41]  M. Henkel,et al.  Superuniversality in phase-ordering disordered ferromagnets , 2008, 0807.1485.

[42]  Peter Sollich,et al.  Glassy dynamics of kinetically constrained models , 2002, cond-mat/0210382.

[43]  Geometry of phase separation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Saleur,et al.  Exact determination of the percolation hull exponent in two dimensions. , 1987, Physical review letters.

[45]  Fisher,et al.  Nonequilibrium dynamics of spin glasses. , 1988, Physical review. B, Condensed matter.

[46]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[47]  Experimental test of curvature-driven dynamics in the phase ordering of a two dimensional liquid crystal. , 2008, Physical review letters.

[48]  L. Cugliandolo,et al.  Scaling and super-universality in the coarsening dynamics of the 3D random field Ising model , 2008, 0803.0664.

[49]  F. Y. Wu.  The Potts model , 1982 .

[50]  Large-q asymptotics of the random-bond potts model , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[51]  Malte Henkel,et al.  Critical phenomena: 150 years since Cagniard de la Tour , 2009 .

[52]  S. Redner,et al.  Freezing into stripe states in two-dimensional ferromagnets and crossing probabilities in critical percolation. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Growing correlations and aging of an elastic line in a random potential , 2009, 0903.4878.

[54]  Jeferson J Arenzon,et al.  Domain growth morphology in curvature-driven two-dimensional coarsening. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  H. Hinrichsen.  Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[56]  J. Stavans,et al.  The evolution of cellular structures , 1993 .

[57]  David P. Landau,et al.  Phase transitions and critical phenomena , 1989, Computing in Science & Engineering.

[58]  Rao,et al.  Kinetics of domain growth in a random-field model in three dimensions. , 1993, Physical review letters.