Phase transitions in the two-dimensional ferro- and antiferromagnetic potts models on a triangular lattice

The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.     

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.     

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.     

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.     

EXACT RESULTS ON THE ANISOTROPIC BOND-DILUTED POTTS MODEL

We propose a new Potts model, anisotropic bond-dilutedPotts model on square lattice. The interactions along x and y directions in this model are generally unequal and the bond-odcupied probabilities in two directions are also assumed to be different. Such a model is a general Potts model on the square lattice. By establishing the equivalence between anisotropic bond-diluted model and anisotropic regular model and making use of the exact critical relations of regular model, we obtain the critical conditions for anisotropic bond-diluted Potts models with ferromagnetic and antiferromagnetic interactions. Phase diagrams according to these conditions are presented numerically with q=1,2,3,4,5,6 (ferr. case) and q=1,1.5,2,2.5 (antiferr. case) and a discussion about these diagrams is carried out.     

Phase diagram of the one-state potts model on the Cayley tree

The phase diagram of the one-state Potts model on the closed asymmetric Cayley tree with branching ratior=2 is obtained from the Bethe-Peierls map. The route to chaos, via the period doubling cascade, is obtained by considering the antiferromagnetic coupling limit. The connection of the Potts model with the percolation problem is shown by calculating the order parameter, its susceptibility, the internal energy, and the specific heat as well as their asymptotic behavior at the paramagnetic-ferromagnetic critical point. Due to the type of the lattice and to the polynomial character of the map, this is the simplest known example of a McKay-Berker-Kirkpatrick spin-glass.     

Computer Simulation of Critical Behavior of Two-Dimensional Weakly Diluted Antiferromagnetic Potts Model on a Triangular Lattice

Physics of the Solid State - The critical behavior of a two-dimensional weakly diluted antiferromagnetic Potts model with spin states q = 3 on a triangular lattice is computationally simulated. The...     

High-temperature series analysis of the p-state Potts glass model on d-dimensional hypercubic lattices

We analyze recently extended high-temperature series expansions for the “Edwards-Anderson” spin-glass susceptibility of the p-state Potts glass model on d-dimensional hypercubic lattices for the case of a symmetric bimodal distribution of ferro- and antiferromagnetic nearest-neighbor couplings . In these star-graph expansions up to order 22 in the inverse temperature , the number of Potts states p and the dimension d are kept as free parameters which can take any value. By applying several series analysis techniques to the new series expansions, this enabled us to determine the critical coupling K_c and the critical exponent of the spin-glass susceptibility in a large region of the two-dimensional (p,d)-parameter space. We discuss the thus obtained information with emphasis on the lower and upper critical dimensions of the model and present a careful comparison with previous estimates for special values of p and d. Received: 25 May 1998 / Revised and Accepted: 11 August 1998     

Magnetic Properties and Antiferromagnetic Coupling in Inhomogeneous Zn1-xFexO Magnetic Semiconductor

Zn1-xFexO inhomogeneous oxide magnetic semiconductor films with high Fe concentration are prepared by sputtering, and fast annealing is carried out at different temperatures. It is found that magnetic properties are greatly modulated by controlling the composition inhomogeneity and subsequently fast annealing. Both ferromagnetic and paramagnetie components are found to coexist in the as-deposited Zn1-xFexO magnetic semiconductor. In particular, the antiferromagnetic coupling between the neighbouring local ferromagnetic regions is found in the as-deposited Zn0.23Fe0.77O film, and the antiferromagnetic coupling strength increases with increasing temperature from 110K to 300 K. We believe that this unusual antiferromagnetic coupling is mediated by thermally activated hopping carriers.     

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.     

Ground-state properties of the antiferromagnetic potts model in an external field

The ground-state properties of the antiferromagnetic q-state Potts model in an external field are studied. At the upper critical field this model may be mapped onto a hard-core lattice gas with activity z = q ?1. This allows us to get some exact results for the triangular lattice on which the corresponding hard hexagon problem has been recently solved by Baxter.     

TheXY model and the three-state antiferromagnetic Potts model in three dimensions: Critical properties from fluctuating boundary conditions

We present the results of a Monte Carlo study of the three-dimensionalXY model and the three-dimensional antiferromagnetic three-state Potts model. In both cases we compute the difference of the free energies of a system with periodic and a system with antiperiodic boundary conditions in a neighborhood of the critical coupling. From the finite-size scaling behaviour of this quantity we extract values for the critical temperature and the critical exponentv that are compatible with recent high-statistics Monte Carlo studies of the models. The results for the free energy difference at the critical temperature and for the exponentv confirm that both models belong to the same universality class.     

Antiferromagnetic Potts Model on the Erdős-Rényi Random Graph

We study the antiferromagnetic Potts model on the Poissonian Erd?s-Rényi random graph. By identifying a suitable interpolation structure and an extended variational principle, together with a positive temperature second-moment analysis we prove the existence of a phase transition at a positive critical temperature. Upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution (recovered in the framework of Derrida-Ruelle probability cascades) and from an entropy positivity argument.     

Angle Integrated Photoemission Study of SmO0.85F0.15FeAs

The electronic structure of the new superconductor SmO_1-xF_xFeAs (x=0.15) is studied by angle-integrated photoemission spectroscopy. Our data show a sharp feature very close to the Fermi energy, and a relative flat distribution of the density of states between 0.5eV and 3eV binding energy, which agrees well with the band structure calculations considering an antiferromagnetic ground state. No noticeable gap opening is observed at 12K below thesuperconducting transition temperature, indicating the existence of large ungapped regions in the Brillouin zone.     

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.     

Ferroelectric Properties of Polycrystalline Ceramics with Dipolar Defect Simulated from the Potts--Ising Model

Physical properties of polycrystailine ferroelectrics including the contributions of the fixed dipolar defects and the average grain size in the Potts-Ising model are simulated by using the Monte Carlo method. Domain pattern, hysteresis loop and switching current of the polarization reversal process are obtained. Two processes are considered in our simulation. In the first one, the grain texture of ferroelectric ceramics are produced from the Ports model, and then the Ising model is implemented in the obtained polycrystailine texture to produce the domain pattern, hysteresis loop and switching current. It is concluded that the defect has the ability to decrease the remnant polarization P~ as well as the coercive field E~. The back switching is obviously observed after the electric field is off, and it shows some variation after introducing the fixed dipolar defect. Meanwhile, the spike of the switching current is found to lower with the increasing defect concentration and the decreasing average grain size.     

Magnetic contribution to the Gibbs energy of elements versus temperature and pressure

A model for the pressure and temperature dependence of the magnetic contributions to the Gibbs energy of ferromagnetic and antiferromagnetic elements is presented. These contributions are described by three parameters: (1) a critical temperature which is represented by the Curie temperature for ferromagnetic elements or Néel temperature for antiferromagnetic elements, (2) the pressure dependence of that critical temperature, (3) the average magnetic moment per atom. Using thermal expansion data, all these parameters and consequently the pressure and temperature dependence of the magnetic contribution can be calculated. Nickel, a ferromagnetic element, is used as an example.     

An approximate method for the investigation of the Potts antiferromagnet in zero external field at zero temperature

We calculate the exact ground state degeneracy for the antiferromagnetic q-state Potts model in zero external field at zero temperature for two and three coupled chains. On the basis of these exact results the ground state degeneracy of the square lattice is expressed as an explicit function of q which is found to be a good approximation.     

Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices

The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by the recurrence relation method in the antiferromagnetic Q-state Potts model on the Bethe lattice (at Q < 2) and in the antiferromagnetic Ising model with three-site interaction on the Husimi cactus. The Lyapunov exponents have been calculated, modulated phases and a chaotic regime in the cyclic period-3 window have been found for one-dimensional rational mappings determined the properties of these systems.     

The inversion relation method for some two-dimensional exactly solved models in lattice statistics

The partition-functions-per-site of several two-dimensional models (notably the eight-vertex, self-dual Potts and hard-hexagon models) can be easily obtained by using an inversion relation for local transfer matrices, together with symmetry and analyticity properties. This technique is discussed, the analyticity properties compared, and some equivalences (and nonequivalences) pointed out. In particular, the critical hard-hexagon model is found to have the same as the self-dualq-state Potts model, withq=(3 + 5)/2 = 2.618 .... The Temperley-Lieb equivalence between the Potts and six-vertex models is found to fail in certain nonphysical antiferromagnetic cases.