• critical dynamics
• Z2 gauge theory
• relaxational dynamics
• dynamic critical exponent

In the context of continuous phase transition, one of the emerging phenomena is the so-called critical slowing down. As the name suggests, it is a slowing down of the dynamics when the system approaches the critical point, developing a diverging characteristic time scale \tau_{c}. These behaviors are described by a universal critical exponent, named z, which controls the diverging of the time scale, i.e. \tau_{c}\sim\xi^{z}, where \xi is the diverging correlation length.

Although critical dynamics has been largely investigated in spin models, such as O(N) spin models, much less is known about the critical dynamics of lattice gauge theories. For this reason, in this work I study the purely relaxational dynamics (model A) of one of the simplest lattice gauge theories: the three-dimensional Z_{2} gauge theory. This gauge theory is known to be one of the earliest models to exhibit a topological phase transition. Although this transition belongs to the three-dimensional Ising universality class, the same cannot be applied to critical dynamics. In particular, I performed Monte Carlo simulations of the three-dimensional Z_{2} gauge model on the simple cubic lattice, with periodic boundary conditions and at the critical point, by using the Metropolis-Hasting algorithm. The rationale behind the choice of this algorithm is that it describes precisely the dynamics we are interested in. In order to reduce the time required by Monte Carlo simulations, I used a multi-spin coding scheme. The goal of this work is to compute the dynamic critical exponent z of the model. For this purpose, I analyze the finite-size scaling of suitably defined time scales, obtaining z=2.63(3). As a test, I apply these methods also on the well-known two-dimensional Ising model, obtaining results perfectly consistent with the current best estimate of its dynamic critical exponent.