• critical phenomena
• Ising model
• relaxational flow
• Monte Carlo simulation
• out-of-equilibrium

In this thesis, we study the out-of-equilibrium dynamics at classical phase transitions arising from a sudden quench of the temperature in Ising models, transitioning from a high-temperature disordered phase to criticality. In particular, we consider purely relaxational dynamics without conserved order parameters. From a theoretical standpoint, we examine the systems within the Renormalization Group (RG) framework, incorporating Finite Size Scaling (FSS) extended to dynamic cases.

From a numerical perspective, we investigate the systems using Monte Carlo simulations, focusing on the 2-dimensional Ising model with Metropolis upgrades for dynamics and the Wolff algorithm to decorrelate starting configurations. We analyze the FSS behavior of observables primarily influenced by the singular part of the free energy, such as susceptibility, correlation length, and the Binder cumulant. Particularly, we explore the behavior of the energy density, which has three contributions in the RG framework at equilibrium: from the analytical and non-analytical parts and a logarithmic contribution for systems with log divergence in specific heat.
Under relaxational dynamics, we observe that these contributions can be disentangled, and the asymptotic post-quench dynamic behavior at a fixed time scaling variable appears to receive contributions from the scaling term at equilibrium.