Monte Carlo analysis of critical properties of the two-dimensional randomly site-diluted Ising model via Wang-Landau algorithm

The influence of random site dilution on the critical properties of the two-dimensional Ising model on a square lattice was explored by Monte Carlo simulations with the Wang-Landau sampling. The lattice linear size was L=20-120 and the concentration of diluted sites q=0.1,0.2,0.3. Its pure version displays a second-order phase transition with a vanishing specific heat critical exponent α, thus, the Harris criterion is inconclusive, in that disorder is a relevant or irrelevant perturbation for the critical behaviour of the pure system. The main effort was focused on the specific heat and magnetic susceptibility. We have also looked at the probability distribution of susceptibility, pseudocritical temperatures and specific heat for assessing self-averaging. The study was carried out in appropriate restricted but dominant energy subspaces. By applying the finite-size scaling analysis, the correlation length exponent ν was found to be greater than one, whereas the ratio of the critical exponents (α/ν) is negative and (γ/ν) retains its pure Ising model value supporting weak universality.     

Wang-Landau study of the 3D Ising model with bond disorder

We implement a two-stage approach of the Wang-Landau algorithm to investigate the critical properties of the 3D Ising model with quenched bond randomness. In particular, we consider the case where disorder couples to the nearest-neighbor ferromagnetic interaction, in terms of a bimodal distribution of strong versus weak bonds. Our simulations are carried out for large ensembles of disorder realizations and lattices with linear sizes L in the range L=8-64L=8{-}64. We apply well-established finite-size scaling techniques and concepts from the scaling theory of disordered systems to describe the nature of the phase transition of the disordered model, departing gradually from the fixed point of the pure system. Our analysis (based on the determination of the critical exponents) shows that the 3D random-bond Ising model belongs to the same universality class with the site- and bond-dilution models, providing a single universality class for the 3D Ising model with these three types of quenched uncorrelated disorder.     

Critical behavior of frustrated Josephson junction arrays with bond disorder

The scaling behavior of the current-voltage (IV) characteristics of a two-dimensional proximity-coupled Josephson junction array (JJA) with quenched bond disorder was investigated for frustrations f = 1/5, 1/3, 2/5, and 1/2. For all these frustrations including 1/5 and 2/5 where a strongly first-order phase transition is expected in the absence of disorder, the IV characteristics exhibited a good scaling behavior. The critical exponent nu indicates that bond disorder may drive the phase transitions to be continuous but not into the Ising universality class, contrary to what was observed in Monte Carlo simulations. The dynamic critical exponent z for JJA's was found to be only 0.60-0.77.     

The effect of quenched bond disorder on first-order phase transitions

We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin–Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in which quantitative numerical simulations can be carried out to investigate emergent criticality due to disorder rounding of first-order transition. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to 128×128$128\times 128$ spins, each of which is represented by three colors taking values ±1$\pm 1$, we show that the rounding of the first-order phase transition is an emergent criticality. We further calculate the correlation length critical exponent, ν$\nu$, and the magnetization critical exponent, β$\beta$, from finite size scaling analysis. We find that the critical exponents, ν$\nu$ and β$\beta$, change as the strength of disorder or the four-spin coupling varies, and we show that the critical exponents appear not to be in the Ising universality class. We know of no analytical approaches that can explain our non-perturbative results. However our results should inspire further work on this important problem, either numerical or analytical.     

Field induced order in magnetic systems: Marginal case

The bond operator representation and the one-loop renormalization group treatment are used to study the spin-1 Heisenberg antiferromagnetic with single-ion anisotropy and transversal magnetic fields in three-dimensional cubic lattices. We start from a disordered spin-liquid phase to an ordered phase, at a critical field H_c1 above which the system enters an XY-antiferromagnetic phase. This transition is interpreted as belonging to a universality class with a dynamical critical exponent z=1. In this marginal case logarithmic corrections are found to the physical quantities. These theoretical predictions are compared with the scaling of the magnetization as a function of field and temperature for the organic compound NiCl₂-4SC(NH₂)₂.     

First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions

We implement a new and accurate numerical entropic scheme to investigate the first-order transition features of the triangular Ising model with nearest-neighbor (J_nn) and next-nearest-neighbor (J_nnn) antiferromagnetic interactions in ratio R=J_nn/J_nnn=1. Important aspects of the existing theories of first-order transitions are briefly reviewed, tested on this model, and compared with previous work on the Potts model. Using lattices with linear sizes L=30,40,…,100,120,140,160,200,240,360 and 480 we estimate the thermal characteristics of the present weak first-order transition. Our results improve the original estimates of Rastelli et al. and verify all the generally accepted predictions of the finite-size scaling theory of first-order transitions, including transition point shifts, thermal, and magnetic anomalies. However, two of our findings are not compatible with current phenomenological expectations. The behavior of transition points, derived from the number-of-phases parameter, is not in accordance with the theoretically conjectured exponentially small shift behavior and the well-known double Gaussian approximation does not correctly describe higher correction terms of the energy cumulants. It is argued that this discrepancy has its origin in the commonly neglected contributions from domain wall corrections.     

Behavior of the antiferromagnetic phase transition near the fermion condensation quantum phase transition in YbRh2Si2

Low-temperature specific-heat measurements on YbRh₂Si₂ at the second order antiferromagnetic (AF) phase transition reveal a sharp peak at TN=72 mK. The corresponding critical exponent α turns out to be α=0.38, which differs significantly from that obtained within the framework of the fluctuation theory of second order phase transitions based on the scale invariance, where α?0.1. We show that under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point leading to a violation of the critical universality of the fluctuation theory. This change of the phase transition is generated by the fermion condensation quantum phase transition. Near the tricritical point the Landau theory of second order phase transitions is applicable and gives α?1/2. We demonstrate that this value of α is in good agreement with the specific-heat measurements.     

Critical behavior near the paramagnetic to ferromagnetic phase transition temperature in La0.7Pb0.05Na0.25MnO3

Critical behavior in La_0.7Pb_0.05Na_0.25MnO₃ has been investigated by dc magnetization measurements. Magnetic data indicate that the compound exhibits a continuous (second-order) paramagnetic (PM) to ferromagnetic (FM) phase transition. Estimates of critical exponents yield δ=4.80±0.01, γ=1.296±0.002 and β=0.344±0.007 (consistent with both the predictions for the three-dimensional-Heisenberg model and with those reported for materials when the FM transition is ascribed to the double exchange (DE) mechanism as a major origin) with T_C=334.54±0.08. The critical exponent γ is slightly inferior than predicted from the 3D Heisenberg model. Such a difference may be due, within the context of the quenched disorder, to the presence of some alterations of short-range magnetic order of FM clusters in the PM phase. The temperature variation in the effective exponent (γ_eff) is similar to those for disordered ferromagnets.     

Phase diagram of the Ising antiferromagnet with nearest-neighbor and next-nearest-neighbor interactions on a square lattice

The phase diagram of the Ising model in the presence of nearest-neighbor (J₁) and next-nearest-neighbor (J₂) interactions on a square lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in finite cluster (we have chosen N=4 spins). We have proposed a functional for the free energy (similar to Landau expansion) to obtain the phase diagram in the (T,α) space (α=J₂/J₁), where the transition line from the superantiferromagnetic (SAF) to the paramagnetic (P) phase is of first-order in the range 1/2<α<0.95 in contrast to previous study of CVM (Cluster Variational Method) that predict first-order transition for α=1.0. Our results for α=1.0 are in accordance with MC (Monte Carlo) simulations, that predict a second-order transition.     

Universality of 3D percolation exponents and first-order corrections to scaling for conductivity exponents

By using a fast, Nested Dissection algorithm we compare the results of finite-size scaling at p_c and of “p” scaling () on large cubic random resistor networks [up to 500×500×500]. The “p” scaling for conductivity of both site and bond networks leads to an exponent t=2.00(1). The finite-size scaling leads to the ratio of this conductivity exponent to the coherence length exponent ν: t/ν=2.283(3). Combining these results we estimate ν=0.876(6), in excellent agreement with a value proposed by Ballesteros et al. The first-order correctional exponent ω is found to be ω=1.0(2).     

Phase transitions and critical properties of the frustrated Heisenberg model on a layer triangular lattice with next-to-nearest-neighbor interactions

The critical behavior of the three-dimensional antiferromagnetic Heisenberg model with nearest-neighbor (J) and next-to-nearest-neighbor (J ₁) interactions is studied by the replica Monte Carlo method. The first-order phase transition and pseudouniversal critical behavior of this model are established for a small lattice in the interval R = |J ₁/J| = 0?C0.115. A complete set of the main static magnetic and chiral critical indices is calculated in this interval using the finite-dimensional scaling theory.     

Temperature dependence of pressure broadening of NH3 perturbed by H2 and N2

The temperature dependence of pressure broadening of 134 rovibrational transitions of several branches in the ν₄ and 2ν₂ bands of ammonia perturbed by H₂ and N₂ has been measured using a high-resolution Fourier transform spectrometer. The temperature range covered during the experiments was between 235 and 296 K. The pressure-broadening linewidths were obtained using the method of multipressure fitting to the measured shapes of the lines. These broadenings were also calculated using a semiclassical model leading to a reasonable agreement with the observations and reproduces well the strong systematic experimental J and K quantum number dependencies. The retrieved values of the linewidths, along with those previously determined from the spectra at room temperature, were used to derive the temperature dependence of both H₂ and N₂ broadening of NH₃ lines. The broadening coefficients were shown to fit closely the well-known exponential law. For both experimental and theoretical results, the temperature exponent n has been obtained. Careful inspection of the experimental values shows that, contrary to the linewidths, the coefficient n is nearly K independent within each J multiplet. Also for a given J it does not seem to exhibit any noticeable variation with the type of rotational transition. On the other hand, the calculated n values exhibit a strong J and K systematic dependencies. n increases with K for a given J, decreases with J for a given K and are independent of the type of rotational transition.     

Phase transitions in adsorbed films of barium on W(011)

Phase transitions in barium submonolayers adsorbed on W(011) are studied in a wide range of temperatures and coverages by the LEED technique, including the temperature measurement of the diffraction intensity. The regions of ordered and disordered structures are determined, the result is presented in the form of phase diagram. The temperature dependence of the adfilm Bragg intensity in the low temperature limit (the lowest temperature is 5 K) shows an appreciable slope for all incoherent and almost all coherent structures, except for (3×2). The fact is discussed in terms of the adfilm long- and quasi-long-range order. The disordering of the (3 × 2) lattice near T_c=130 K is the second-order phase transition with the order parameter critical exponent β=0.16. the adfilm is two-phase in the range n=(3.2?3.8)×10¹⁴cm^?2 and singlehase for the rest of the coverages. The effect of the first-order phase transition on the character of the work function change in the two-phase region is discussed.     

Three-state majority-vote model on square lattice

Here, a non-equilibrium model with two states (−1,+1) and a noise q on simple square lattices proposed for M.J. Oliveira (1992) following the conjecture of up-down symmetry of Grinstein and colleagues (1985) is studied and generalized. This model is well-known, today, as the majority-vote model. They showed, through Monte Carlo simulations, that their obtained results fall into the universality class of the equilibrium Ising model on a square lattice. In this work, we generalize the majority-vote model for a version with three states, now including the zero state, (−1,0,+1) in two dimensions. Using Monte Carlo simulations, we showed that our model falls into the universality class of the spin-1 (−1,0,+1) and spin-1/2 Ising model and also agree with majority-vote model proposed for M.J. Oliveira (1992). The exponent ratio obtained for our model was γ/ν=1.77(3), β/ν=0.121(5), and 1/ν=1.03(5). The critical noise obtained and the fourth-order cumulant were q_c=0.106(5) and U^∗=0.62(3).     

Effects of divalent impurities on the fluctuation conductivity of YBa2Cu3O7 single crystals

We have studied experimentally the in-plane fluctuation conductivity near the superconducting transition in single crystal samples of YBa₂Cu₃O₇, Y_0.98Ca_0.02Ba₂Cu₃O₇, YBa_1.9Sr_0.1Cu₃O₇ and YBa₂Cu_2.97Zn_0.03O₇. In order to test the stability of the observed fluctuation regimes, low magnetic fields were applied perpendicular to the Cu-O₂ atomic planes. When the transition is approached from above we first observe a three-dimensional (3D) Gaussian regime then a crossover to a genuine critical region where the exponent is consistent with the predictions of the 3D-XY-E universality class. Decreasing further the temperature towards T_c, our results systematically reveal the occurrence of a regime beyond 3D-XY characterized by a very small critical exponent. We propose that this regime is precursory to a weak first-order superconducting transition driven by antiferromagnetic excitations related to the pseudogap phenomenon. The dilution of divalent impurities in YBa₂Cu₃O₇ does not affect the stability of the fluctuation regime beyond 3D-XY and in the case of Ca doping a further approach towards the first-order behaviour is observed.     

Phase transition analysis in Z2 and U(1) lattice gauge theories

The transition region of Z₂ lattice gauge theory is investigated by inverting the strong coupling series of the average plaquette energy E_P(J). We find a clear evidence for a first-order transition and the existence of a metastable phase. In the U(1) case we confirm a second-order phase transition even if there is a little discrepancy on the critical point position as indicated by Monte Carlo simulations.     

Frustrated model to describe reentrant behavior in copper oxide superconductors

The quenched decorated Ising model with competitive interactions is used here to described the magnetic properties of the copper oxide superconductors compounds in the insulating phase (antiferromagnetic). The model consists of planes in which the nodal spins interact antiferromagnetically (J_A<0) with their nearest-neighbors, and ferromagnetically (J_F>0) with the spins that decorate the bonds, which are quenched and distributed randomly over the two-dimensional lattice. The planes interact antiferromagnetically with weak-exchange interaction (i.e., , λ=10^-5). By using the framework of an effective-field theory, based on the differential operator technique, we discuss the antiferromagnetic-phase stability limit in the temperature-decorated bond concentration space (T-p), for λ=10^-5 and various values of frustration parameter α=J_A/J_F. For certain region range of the parameter α we observe a reentrant behavior at low-temperature. We also discuss the critical behavior of T_N versus α for some values of decorated bond concentrations and reentrant phenomena is observed. We calculate the dependence of the staggered magnetization as a function of the temperature to analyze the reentrant behavior observed in the phase diagrams.     

Critical properties of the three-dimensional Ising model with quenched disorder

The static critical properties of the three-dimensional Ising model with quenched disorder are studied by the Monte-Carlo (MC) method on a simple cubic lattice, in which the quenched disorder is distributed as nonmagnetic impurities by the canonical manner. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.0; 0.95; 0.9; 0.8; 0.7; 0.6. The systems of non-linear sizes L×L×L, L=20-60 are researched. On the basis of the finite-size scaling (FSS) theory, the static critical exponents of specific heat α, susceptibility γ, magnetization β, and an exponent of the correlation radius in a studied interval of concentrations p are calculated. It is shown that the three-dimensional Ising model with quenched disorder has two regimes of the critical behavior universality in a dependence on nonmagnetic impurities.     

Thermodynamic quantum critical behavior of the anisotropic Kondo necklace model

The Ising-like anisotropy parameter δ in the Kondo necklace model is analyzed using the bond-operator method at zero and finite temperatures for arbitrary d dimensions. A decoupling scheme on the double time Green's functions is used to find the dispersion relation for the excitations of the system. At zero temperature and in the paramagnetic side of the phase diagram, we determine the spin gap exponent νz≈0.5 in three dimensions and anisotropy between 0?δ?1, a result consistent with the dynamic exponent z=1 for the Gaussian character of the bond-operator treatment. On the other hand, in the antiferromagnetic phase at low but finite temperatures, the line of Neel transitions is calculated for δ?1. For d>2 it is only re-normalized by the anisotropy parameter and varies with the distance to the quantum critical point (QCP) |g| as, T_N∝|g|^ψ where the shift exponent ψ=1/(d-1). Nevertheless, in two dimensions, a long-range magnetic order occurs only at T=0 for any δ?1. In the paramagnetic phase, we also find a power law temperature dependence on the specific heat at the quantum critical trajectoryJ/t=(J/t)_c, T→0. It behaves as C_V∝T^d for δ?1 and ≈1, in concordance with the scaling theory for z=1.