Monte Carlo study of the phase transitions in 2D ferro- and antiferromagnetic Potts models on a triangular lattice

The phase transitions in 2D ferro- and antiferromagnetic Potts models with number of spin states q = 3 on a triangular lattice are investigated by the cluster and classical Monte Carlo methods. Systems with linear sizes L = 20–120 are considered. Fourth-order Binder cumulants and histogram data analysis are used to show that second- and first-order phase transitions are observed in the ferromagnetic and antiferromagnetic Potts models, respectively. The static critical indices are calculated for specific heat α, susceptibility γ, magnetization β, and correlation length ν on the basis of finite-size scaling theory for a ferromagnetic Potts model.     

Histogram data analysis for a three-dimensional diluted ferromagnetic 3- and 4-state potts models

On the basis of a histogram data analysis, phase transitions (PTs) in a three-dimensional diluted ferromagnetic 3- and 4-state Potts models are investigated. Systems with linear dimensions of L = 20–60 and spin concentrations of p = 1.00, 0.95, and 0.65 are studied. It is shown that the introduction of weak disorder (p ～ 0.95) into the system in the three-dimensional Potts model with q = 3 is sufficient to change a first-order phase transition to a second-order one, whereas, in the three-dimensional Potts model with q = 4, the change of a first-order phase transition to a second-order one occurs only in the presence of strong disorder (p ～ 0.65).     

On Dynamical Systems and Phase Transitions for q + 1-state p-adic Potts Model on the Cayley Tree

In the present paper, we study a new kind of p-adic measures for q?+?1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition.     

New Heusler alloys with a metamagnetostructural phase transition

Investigations of new ferromagnetic shape-memory Ni-Mn-Z Heusler alloys (Z = In, Sn, Sb) are reviewed. Experimental data are described and explained on the assumption that these alloys undergo a phase transition from the ferromagnetic to the antiferromagnetic state (metamagnetic transition). The results of theoretical studies of the phase diagrams of these alloys are considered with regard to the possible change in the character of magnetic ordering (from ferromagnetic to antiferromagnetic) and interaction of the structural martensitic transformation with the metamagnetic transition.     

The Phase Transition in the Three-State Potts Model: An Analytical Analysis

Weinvestigate thephase transition of the three-state Potts model in an analytical approachthe generalized cumtilant expansion with the effective mean field Itypothesis. We find a first order phase transition in the three-dimensional three-state Pot ts model with ferromagnetic nearest neighbor (nn) coupling. For the model with antiferromagnetic next-to-nearest neighbor (nnn) coupling, pe find a first order transition when tlle relative strength of the nnncoupling γ is fixed to -0.2. The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.     

Potts Model on Maple Leaf Lattice with Pure Three-Site Interaction

We use Monte Carlo method to study three-state Potts model on maple leaf lattice with pure three-site interaction. The critical behavior of both ferromagnetic and antiferromagnetic cases is studied. Our results confirm that the critical behavior of the ferromagnetic model is independent of the lattice details and lies in the universality class of the three-state ferromagnetic Potts model. For the antiferromagnetic case the transition is of the first order. We have calculated the energy jump and critical temperature in this area. We find there is a tricritical point separating the first order and second order phases for this system.     

Investigation of the influence of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model

The influence of quenched nonmagnetic impurities on phase transitions in the three-dimensional Potts model with the number of spin states q = 3 is investigated using the Wolff single-cluster algorithm of the Monte Carlo method. The systems with linear sizes L = 20–44 at the spin concentrations p = 1.0, 0.9, 0.8, and 0.7 are analyzed. It is demonstrated with the use of the method of fourth-order Binder cumulants that the second-order phase transition occurs in the model under consideration at the spin concentrations p = 0.9, 0.8, and 0.7 and that the first-order phase transition is observed in the pure model (p = 1.0). The static critical exponents α (heat capacity), γ (susceptibility), β (magnetization), and ν (correlation length) are calculated in the framework of the finite-size scaling theory. The problem regarding the universality classes of the critical behavior of weakly diluted systems is discussed.     

Investigation of the Potts Model on Triangular Lattices by the Second Renormalization of Tensor Network States

We employ the second renormalization group method of tensor-network states to investigate thermodynamic properties of the ferromagnetic and antiferromagnetic Potts model on triangular lattices. From the temperature dependence of the internal energy and the specific heat, both the critical temperatures and critical exponents are evaluated. For the q = 3 antiferromagnetic Potts model, the critical temperature is found to be Tc = 0.627163±0.000003, which is at least one order of magnitude more accurate than that obtained by other methods.     

Phase transitions in the two-dimensional antiferromagnetic Potts model on a triangular lattice

Phase transitions and thermodynamic properties in the two-dimensional three-state antiferromagnetic Potts model on a triangular lattice are investigated using the Monte Carlo method and the histogram analysis of the data. It is shown that pronounced first-order phase transitions are observed in this model for systems with rather large linear dimensions (L > 120). No first-order PTs are observed for systems with L < 120.     

Phase transitions in three-dimensional three-state Potts model

We have performed a Monte Carlo investigation of the nature of the phase transition in the three-state, three-dimensional Potts model with nearest and next nearest neighbour coupling. We find strong evidence for a first-order phase transition in the case of ferromagnetic coupling. In the case of a first neighbour ferromagnetic coupling and second neighbour antiferromagnetic, there is evidence for a second-order transition. This result supports the idea that a second-order transition can be present in systems which, according to the Landau criterium, should only undergo a first-order transition.     

Triangular lattice Potts models

In this paper we study the 3-state Potts model on the triangular lattice which has two- and three-site interactions. Using a Peierls argument we obtain a rigorous bound on the transition temperature, thereby disproving a conjecture on the location of its critical point. Low-temperature series are generated and analyzed for three particular choices of the coupling constants; a phase diagram is then drawn on the basis of these considerations. Our analysis indicates that the antiferromagnetic transition and the transition along the coexistence line are of first order, implying the existence of a multicritical point in the ferromagnetic region. Relation of the triangularq-state Potts model with other lattice-statistical problems is also discussed. In particular, an Ashkin-Teller model and the hard-hexagon lattice gas solved by Baxter emerge as special cases in appropriate limits.Supported in part by NSF grant No. DMR 78-18808.     

The antiferromagnetic Potts model in two dimensions: Berker-Kadanoff phase, antiferromagnetic transition, and the role of Beraha numbers

Using methods of integrable systems and conformal field theory, we study the Q-state Potts model on the square lattice with e^K real. We discover a surprisingly rich phase diagram that involves, besides the usual ferromagnetic critical line, an antiferromagnetic critical line and a Berker-Kadanoff phase (i.e., a massless low-temperature phase with coupling-independent exponents) that has singularities at the Baraha numbers (including Q integer) Q = 4cos²π/n. Critical properties are derived; we show in particular that the Q = 4cos²π/δ antiferromagnetic critical Potts model is in the “Z_δ−2” universality class with c = 2−6/δ. Extensions to other lattices are considered. We discuss the consequences of our results on the coloring problem and the Beraha conjecture. Three appendices deal with the geometrical interpretation of the Temperley-Lieb algebra and U_qsl(2) symmetry in the Potts and associated loops model, and with the vertex-Potts model correspondence in systems with free boundary conditions.     

Phase transitions in the 2D J 1-J 2 Heisenberg model with arbitrary signs of exchange interactions

The ground state of the J ₁-J ₂ Heisenberg model with arbitrary signs of exchange is studied for spin S = 1/2 in the case of the two-dimensional (2D) square lattice. The states with different types of spin long-range order (antiferromagnetic checkerboard, stripe, collinear ferromagnetic) as well as the disordered spin liquid states are described in the framework of one analytical approach. In particular, it is shown that the phase transition between the ferromagnetic spin liquid and the ferromagnet with long-range order is of the second order. In the vicinity of such transition, we have found the ferromagnetic state with a rapidly varying condensate function.     

Ashkin-teller criticality and pseudo-first-order behavior in a frustrated Ising model on the square lattice

We study the challenging thermal phase transition to stripe order in the frustrated square-lattice Ising model with couplings J(1) < 0 (nearest-neighbor, ferromagnetic) and J(2) > 0 (second-neighbor, antiferromagnetic) for g = J(2)/|J(1| > 1/2. Using Monte Carlo simulations and known analytical results, we demonstrate Ashkin-Teller criticality for g ≥ g*; i.e., the critical exponents vary continuously between those of the 4-state Potts model at g = g* and the Ising model for g → ∞. Thus, stripe transitions offer a route to realizing a related class of conformal field theories with conformal charge c = 1 and varying exponents. The transition is first order for g < g* = 0.67 ± 0.01, much lower than previously believed, and exhibits pseudo-first-order behavior for |g* ≤ g 相似文献   

The spin-peierls critical temperature in an XY quasi-one-dimensional system with nearest and next-nearest neighbour interactions

The mean field critical temperature for the spin-Peierls phase transition in the XY antiferromagnetic chain is obtained for nearest and next nearest neighbour exchange interaction. An increase in T_c is predicted for next nearest neighbour antiferromagnetic exchange and a decrease is obtained for ferromagnetic exchange. This model is applied to the alkali-TCNQ salts, which are treated in the framework of the highly correlated Hubbard model.     

Critical exponents of the 3D antiferromagnetic three-state Potts model using the coherent-anomaly method

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using the coherent-anomaly method (CAM). The CAM analysis provides the estimates for the critical exponents which indicate the XY universality class, namely α = −0.011, β = 0.351, γ = 1.309 and δ = 4.73. This observation corroborates the results of the recent Monte Carlo simulations, and disagrees with the proposal of a new universality class.     

Investigation of the critical behavior of the three-dimensional weakly diluted Potts model

The static critical behavior of the three-dimensional weakly diluted Potts model with the state q = 3 on a simple cubic lattice has been investigated by the Monte Carlo method using the Wolff single-cluster algorithm. It is shown that at the spin concentrations p = 0.9 and 0.8 a second-order phase transition is observed in the three-dimensional weakly diluted Potts model with the state q = 3. On the basis of the finite-size scaling theory, we calculated the static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the correlation-length exponent v.     

Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model

The phase transitions and critical phenomena in the three-dimensional (3D) site-diluted q-state Potts models on a simple cubic lattice are explored. We systematically study the phase transitions of the models for q=3 and q=4 on the basis of Wolff high-effective algorithm by the Monte–Carlo (MC) method. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.00–0.65. It is shown that introducing of weak disorder (p∼0.95) into the system is sufficient to change the first order phase transition into a second order one for the 3D 3-state Potts model, while for the 3D 4-state Potts model, such a phase transformation occurs when introducing strong disorder (p∼0.65). Results for 3D pure 3-state and 4-state Potts models (p=1.00) agree with conclusions of mean field theory. The static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the exponent of the correlation radius ν are calculated for the samples on the basis of finite-size scaling theory.     

Transition De Phase Metamagnetique Du Bromure Ferreux

In a magnetic field parallel to the magnetization axis of an antiferromagnetic Fe Br₂ single crystal, a caracteristic metamagnetic behaviour is observed. The transition from an antiferromagnetic phase to a paramagnetic phase is studied by help of magnetization measurements in a steady field (H < 60 kOe). The measurement precision has allowed a detailed study of the magnetization isotherms, caracteristic of a first order magnetization phase transition (T < T_c = 4, 7 K) and of a second order phase transition (T_c < T < T_N = 14, 2 K).We have observed an original phase diagram. In a certain temperature and field range, the ordered phase is stable on the high temperature side of the transition point. Some theoretical studies in an Ising model, or in the hypothesis of a strong magnetoelastic coupling forecast the existence of such a magnetic phase diagram.At present, we proceed to a theoretical study, in a molecular field approximation, of the magnetic phase diagram of compounds similar to Fe Br₂ where we take into account the relative values of parameters J₁, J₂ and D associated with ferromagnetic and antiferromagnetic interactions and crystalline anisotropy.     

Magnetic properties of the Nd0.9MnOx cation-deficient manganites

This paper reports on the results of x-ray diffraction and magnetic studies of manganites in the Nd_0.9MnO_x system with an oxygen content varying in the range 2.84 < x < 2.93. A sample with an oxygen content x = 2.84 undergoes a first-order phase transition at a temperature close to T = 1050 K, whereas an anomaly observed in the elastic properties for a sample with x = 2.93 indicates a phase transition near T ≈ 500 K. It is assumed that these transitions are governed by cooperative ordering of Mn e _g orbitals of the same type as in stoichiometric NdMnO₃. The manganite at an oxygen content x = 2.85 is an antiferromagnet with a Néel temperature T _N = 85 K, whereas the magnetic properties of the manganites at x = 2.90 and 2.93 suggest that an antiferromagnetic component coexists with a ferromagnetic component. The magnetic interaction between the ferromagnetic and antiferromagnetic components manifests itself in the fact that the magnetic moment becomes opposite in direction to the external magnetic field. The properties of the samples are consistent with the hypothesis that part of the neodymium ions (up to 5%) can be substituted for manganese ions.