Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions

We study numerically the phase-ordering kinetics of the site-diluted and bond-diluted Ising models after a quench from an infinite to a low temperature. We show that the speed of growth of the ordered domain's size is non-monotonous with respect to the amount of dilution $D$: Starting from the pure case $D=0$ the system slows down when dilution is added, as it is usually expected when disorder is introduced, but only up to a certain value $D^*$ beyond which the speed of growt...

We study the antiferromagnetic $q$-state Potts model on the square lattice for $q=3$ and $q=4$, using the Wang-Swendsen-Koteck\'y Monte Carlo algorithm and a new finite-size-scaling extrapolation method. For $q=3$ we obtain good control up to correlation length $\xi \sim 5000$; the data are consistent with $\xi(\beta) = A e^{2\beta} \beta (1 + a_1 e^{-\beta} + \ldots)$ as $\beta\to\infty$. For $q=4$ the model is disordered even at zero temperature.

It is demonstrated that the scaled order parameter for ferromagnetic Ising and three-state Potts chains with inverse-square interactions exhibits a universal critical jump, in analogy with the superfluid density in helium films. Renormalization-group arguments are combined with numerical simulations of systems containing up to one million lattice sites to accurately determine the critical properties of these models. In strong contrast with earlier work, compelling quantitativ...

We study some analytical properties of the solutions of the non perturbative renormalization group flow equations for a scalar field theory with $Z_2$ symmetry in the ordered phase, i.e. at temperatures below the critical temperature. The study is made in the framework of the local potential approximation. We show that the required physical discontinuity of the magnetic susceptibility $\chi(M)$ at $M=\pm M_0$ ($M_0$ spontaneous magnetization) is reproduced only if the cut-off...

We analyze the critical behaviour of the three-dimensional, three-state Potts model in the presence of an external ordering field. From a finite size scaling analysis on lattices of size up to 70**3 we determine the critical endpoint of the line of first order phase transitions as (b_c, h_c) =(0.54938(2), 0.000775(10)). We determine the relevant temperature like and symmetry breaking directions at this second order critical point and explicitly verify that it is in the univer...

Following the work by Houghton, Reeve and Wallace about an alternative formulation of the $n \to 0 $ limit of the $(n+1)$ state Potts model in field theory for the large order behaviour of the perturbative expansion, we generalise their technique to all $n$ by establishing an equivalence in perturbation theory order by order with another bosonic field theory. Restricting ourselves to a cubic interaction, we obtain an explicit expression (in terms of~$n$) for the large order b...

We study the probability distribution function (PDF) of the order parameter of the three-dimensional $O(N)$ model at criticality using the functional renormalisation group. For this purpose, we generalize the method introduced in [Balog et al., Phys. Rev. Lett. {\bf 129}, 210602 (2022)] to the $O(N)$ model. We study the large $N$ limit, as well as the cases $N=2$ and $N=3$ at the level of the Local Potential Approximation (LPA), and compare our results to Monte Carlo simulati...

Using a novel finite size scaling Monte Carlo method, we calculate the four, six and eight point renormalized coupling constants defined at zero momentum in the symmetric phase of the three dimensional Ising system. The results of the 2D Ising system that were directly measured are also reported. Our values of the six and eight point coupling constants are significantly different from those obtained from other methods.

We investigate the three-state antiferromagnetic Potts model on a simple cubic lattice with a cluster flipping Monte Carlo simulation algorithm in the temperature region below the transition into disorder at T_{c1}. We find both the well established broken-sublattice-symmetry (BSS) phase at low temperature and a new, rotationally symmetric phase at higher temperature, but below T_{c1}. The properties of the second phase and the transition temperature to the BSS phase are in d...

We investigate the low energy properties of Lorentz-invariant theories with a spontaneously broken rotation symmetry O(N) $\to$ O(N--1). The leading coefficients of the low temperature expansion for the partition function are calculated up to and including three loops. Emphasis is put into the special case N=3: it describes the antiferromagnet which has been extensively studied. Our results obtained within the framework of the effective Lagrangian technique are compared with ...