Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization

Abstract

We consider the Langevin lattice dynamics for a spontaneously broken lambda phi^4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.

26 pages, 4 eps figures (Elsevier latex style)

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• Universal scaling of the sigma field and net-protons from Langevin dynamics of model A
• Broadening of the chiral critical region in a hydrodynamically expanding medium
• Dynamical critical fluctuations near the QCD critical point with hydrodynamic cooling rate
• $\eta (T)/s(T)$ and collective flow in chiral hydrodynamics
• Strongly interacting matter in extreme magnetic fields
• Time-dependent Ginzburg-Landau approach to the dynamics of inhomogeneous chiral condensates in a nonlocal Nambu--Jona-Lasinio model
• What happens when supercooling is terminated by curvature flipping of the effective potential?
• Non-equilibrium fluctuations at the QCD phase transition
• Cumulants of the chiral order parameter at lower RHIC energies
• Renormalization of stochastic differential equations with multiplicative noise using effective potential methods