Critical behaviour of the 1D q-state Potts model with long-range interactions

The critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as $r^{-(1+\sigma)}$ has been studied in the wide range of parameters $0 < \sigma \le 1$ and $\frac{1}{16} \le q \le 64$. A transfer matrix has been constructed for a truncated range of interactions for integer and continuous q, and finite range scaling has been applied. Results for the phase diagram and the correlation length critical exponent are presented.Comment: 20 pages plus 4 figures, Late

Critical behavior of the long-range Ising chain from the largest-cluster probability distribution

Monte Carlo simulations of the 1D Ising model with ferromagnetic interactions decaying with distance $r$ as $1/r^{1+\sigma}$ are performed by applying the Swendsen-Wang cluster algorithm with cumulative probabilities. The critical behavior in the non-classical critical regime corresponding to $0.5 <\sigma < 1$ is derived from the finite-size scaling analysis of the largest cluster.Comment: 4 pages, 2 figures, in RevTeX, to appear in Phys. Rev. E (Feb 2001

Quantum oscillations of the magnetic torque in the nodal-line Dirac semimetal ZrSiS

We report a study of quantum oscillations (QO) in the magnetic torque of the nodal-line Dirac semimetal ZrSiS in the magnetic fields up to 35 T and the temperature range from 40 K down to 2 K, enabling high resolution mapping of the Fermi surface (FS) topology in the $k_z=\pi$ (Z-R-A) plane of the first Brillouin zone (FBZ). It is found that the oscillatory part of the measured magnetic torque signal consists of low frequency (LF) contributions (frequencies up to 1000 T) and high frequency (HF) contributions (several clusters of frequencies from 7-22 kT). Increased resolution and angle-resolved measurements allow us to show that the high oscillation frequencies originate from magnetic breakdown (MB) orbits involving clusters of individual $\alpha$ hole and $\beta$ electron pockets from the diamond shaped FS in the Z-R-A plane. Analyzing the HF oscillations we have unequivocally shown that the QO frequency from the dog-bone shaped Fermi pocket ($\beta$ pocket) amounts $\beta=591(15)$ T. Our findings suggest that most of the frequencies in the LF part of QO can also be explained by MB orbits when intraband tunneling in the dog-bone shaped $\beta$ electron pocket is taken into account. Our results give a new understanding of the novel properties of the FS of the nodal-line Dirac semimetal ZrSiS and sister compounds

Short-time dynamics in the 1D long-range Potts model

We present numerical investigations of the short-time dynamics at criticality in the 1D Potts model with power-law decaying interactions of the form 1/r^{1+sigma}. The scaling properties of the magnetization, autocorrelation function and time correlations of the magnetization are studied. The dynamical critical exponents theta' and z are derived in the cases q=2 and q=3 for several values of the parameter $\sigma$ belonging to the nontrivial critical regime.Comment: 8 pages, 8 figures, minor changes - several typos fixed, one reference change

Evidence of exactness of the mean field theory in the nonextensive regime of long-range spin models

The q-state Potts model with long-range interactions that decay as 1/r^alpha subjected to an uniform magnetic field on d-dimensional lattices is analized for different values of q in the nonextensive regime (alpha between 0 and d). We also consider the two dimensional antiferromagnetic Ising model with the same type of interactions. The mean field solution and Monte Carlo calculations for the equations of state for these models are compared. We show that, using a derived scaling which properly describes the nonextensive thermodynamic behaviour, both types of calculations show an excellent agreement in all the cases here considered, except for alpha=d. These results allow us to extend to nonextensive magnetic models a previous conjecture which states that the mean field theory is exact for the Ising one.Comment: 10 pages, 4 figure

The Information Geometry of the One-Dimensional Potts Model

In various statistical-mechanical models the introduction of a metric onto the space of parameters (e.g. the temperature variable, $\beta$, and the external field variable, $h$, in the case of spin models) gives an alternative perspective on the phase structure. For the one-dimensional Ising model the scalar curvature, ${\cal R}$, of this metric can be calculated explicitly in the thermodynamic limit and is found to be ${\cal R} = 1 + \cosh (h) / \sqrt{\sinh^2 (h) + \exp (- 4 \beta)}$. This is positive definite and, for physical fields and temperatures, diverges only at the zero-temperature, zero-field ``critical point'' of the model. In this note we calculate ${\cal R}$ for the one-dimensional $q$-state Potts model, finding an expression of the form ${\cal R} = A(q,\beta,h) + B (q,\beta,h)/\sqrt{\eta(q,\beta,h)}$, where $\eta(q,\beta,h)$ is the Potts analogue of $\sinh^2 (h) + \exp (- 4 \beta)$. This is no longer positive definite, but once again it diverges only at the critical point in the space of real parameters. We remark, however, that a naive analytic continuation to complex field reveals a further divergence in the Ising and Potts curvatures at the Lee-Yang edge.Comment: 9 pages + 4 eps figure

First-order transition in the one-dimensional three-state Potts model with long-range interactions

The first-order phase transition in the three-state Potts model with long-range interactions decaying as $1/r^{1+\sigma}$ has been examined by numerical simulations using recently proposed Luijten-Bl\"ote algorithm. By applying scaling arguments to the interface free energy, the Binder's fourth-order cumulant, and the specific heat maximum, the change in the character of the transition through variation of parameter $\sigma$ was studied.Comment: 6 pages (containing 5 figures), to appear in Phys. Rev.

Criticality in one dimension with inverse square-law potentials

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 quantitative evidence for the Kosterlitz--Thouless-like character of the phase transition is provided.Comment: To appear in Phys. Rev. Let

Reexamination of the long-range Potts model: a multicanonical approach

We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interaction $1/r^{d+\sigma}$, using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value $\sigma_c(q)$ separating the first- and second-order regimes to two-digit precision within the range $3 \leq q \leq 9$. We offer convincing numerical evidence supporting $\sigma_c(q)Comment: 18 pages, 18 figure