We investigate the critical properties of the three-dimensional antiferromagnetic RP^N-1 model, which is characterized by a global O(N) symmetry and a discrete Z_2 gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group flow of the most general Φ^4 theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For N=4 no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of O(N) symmetric models with a discrete Z_2 gauge symmetry.
Criticality of O(N) symmetric models in the presence of discrete gauge symmetries
Tripodo, Antonio;Vicari, Ettore
2018-01-01
Abstract
We investigate the critical properties of the three-dimensional antiferromagnetic RP^N-1 model, which is characterized by a global O(N) symmetry and a discrete Z_2 gauge symmetry. We perform a field-theoretical analysis using the Landau-Ginzburg-Wilson (LGW) approach and a numerical Monte Carlo study. The LGW field-theoretical results are obtained by high-order perturbative analyses of the renormalization-group flow of the most general Φ^4 theory with the same global symmetry as the model, assuming a gauge-invariant order-parameter field. For N=4 no stable fixed point is found, implying that any transition must necessarily be of first order. This is contradicted by the numerical results that provide strong evidence for a continuous transition. This suggests that gauge modes are not always irrelevant, as assumed by the LGW approach, but they may play an important role to determine the actual critical dynamics at the phase transition of O(N) symmetric models with a discrete Z_2 gauge symmetry.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
