Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-11-30
Lect.Notes Phys.716:295-348,2007
Physics
Condensed Matter
Statistical Mechanics
54 pages, 9 figures, Lecture Notes for Luxembourg Summer School "Ageing and the Glass Transition", submitted to Springer Lectu
Scientific paper
10.1007/3-540-69684-9_7
It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale invariance, both near and far from thermal equilibrium. Part 1 introduces the response functional field theory representation of (nonlinear) Langevin equations. The RG is employed to compute the scaling exponents for several universality classes governing the critical dynamics near second-order phase transitions in equilibrium. The effects of reversible mode-coupling terms, quenching from random initial conditions to the critical point, and violating the detailed balance constraints are briefly discussed. It is shown how the same formalism can be applied to nonequilibrium systems such as driven diffusive lattice gases. Part 2 describes how the master equation for stochastic particle reaction processes can be mapped onto a field theory action. The RG is then used to analyse simple diffusion-limited annihilation reactions as well as generic continuous transitions from active to inactive, absorbing states, which are characterised by the power laws of (critical) directed percolation. Certain other important universality classes are mentioned, and some open issues are listed.
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