High pressure hydrogen and the Potts model 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.

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.

Topology of the space of periodic ground states in the antiferromagnetic Ising and Potts models in selected spatial structures

The Monte Carlo method is used to study phase transitions in the two-dimensional Potts model with the number of states spin q = 3 on square and hexagonal lattices. Considered systems with linear dimensions L × L = N, L = 21 ÷ 102. The obtained numerical data indicate that in the considered In the Potts model, a second-order phase transition is observed in accordance with the analytical theory. The Binder cumulants method of the fourth order determines the values ​​of the critical points of the Potts model on different lattices.

The spin Hamiltonian with spin-1 system including a single parameter is proposed which expresses the 3-state Potts model (PM) or antiferromagnetic Potts model (AFPM) according as a value of the parameter. They are investigated by a new method which is the extension of the effective Hamiltonian method in a unified way. The first-order transition or the second-order transition are obtained for the PM or the AFPM, respectively. In the AFPM, the ordered phase has a residual entropy, nevertheless the ordered phase can exist stably.

Toluene Disproportionation and Coke Formation on Mordenites Effect of Catalyst Modifications and of Operating Conditions

This paper describes a study on surface film formation and hydrogen permeation at stainless steel surfaces under high pressure hydrogen. In order to investigate hydrogen permeation into the steels, exposure tests in high pressure hydrogen were conducted with AISI 316 and 316L stainless steel specimens. To determine the concentration of hydrogen in the specimens and characteristics of surface oxide layer, desorption spectra of hydrogen and water were determined with TDS. In addition, XPS analyses were performed to identify chemical composition of the exposed surfaces. It was found that the permeation of hydrogen through the steel surface was related to the desorption behavior of water, which could be originated from the surface film formed during the exposure to high pressure gas.

The kinetics of domain growth for a q=8 state Potts model on a triangular lattice is studied using the Monte Carlo renormalization-group technique. A block-spin transformation is applied to the evolving configurations of a two-dimensional Potts model with nonconserved order parameter. The growth law for the average size of domains is consistent with curvature-driven growth. A scaling form for the structure factor is obtained and compared to theory. The edge distribution function for the growth kinetics is also studied.

Hydrogen can be produced from water electrolysis which can operate at atmospheric pressure or high pressure. Today’s industry including vehicle one, devotes efforts to produce high pressure hydrogen by using pressurized electrolyser. The purpose of this work is to estimate the ideal electrical energy needed for high pressure hydrogen under high pressure water electrolysis conditions. Calculations are based on the estimation of the enthalpy and free Gibbs energy of water electrolysis at various pressures and temperatures, referring to both the work of LeRoy & Onda.

Phase transitions and thermodynamic properties of triangular strongly-diluted antiferromagnetic Potts model

The phase transition of four-state antiferromagnetic Potts model on simple cubic and body-centered-cubic lattice is studied by cluster Monte Carlo simulations of finite systems up to ${96}^{3}$ lattice sizes. The result indicates that the size ${96}^{3}$ is still sufficient to extract asymptotic behavior. However, if one assumes that both models are well described by the usual Ginzburg-Landau Hamiltonian, the result is consistent with the prediction of the field-theoretical analysis that the phase transition is first-order one.

We propose families of infinitely ramified fractals, which we call the m-sheet Sierpinski gasket with side b [(mSG${)}_{\mathit{b}}$], on which the q-state Potts model can be exactly solvable through a real-space renormalization-group (RSRG) technique for which there are phase transitions at finite temperatures for m>1. We also propose, within a cell-to-cell RSRG scheme, a criterion for a suitable choice of cells in the study of antiferromagnetic (AF) classical spin models defined on (or approximated by) multirooted hierarchical lattices, and apply it for the AF Potts model on some (mSG${)}_{\mathit{b}}$ fractals. Concerning the Ising model on the (mSG${)}_{2}$ family, we obtain the exact para (P)--ferromagnetic (F) critical temperature as a function of m and verify that, for m=1 and 2, there is no AF order (not even at zero temperature). We calculated the exact P-F and possibly exact P-AF critical frontiers and the corresponding correlation-length critical exponents for q=2-, 3-, and 4-state Potts model on the (mSG${)}_{4}$. The AF q=2 and 4 cases have highly degenerate ground states and each one presents, above a certain critical fractal dimension ${\mathit{D}}_{\mathit{f}}^{\mathit{c}}$(q,m), an unusual low-temperature phase whose attractor occurs at a non-null temperature. For q=2 and ${\mathit{D}}_{\mathit{f}}$(2,m)\ensuremath{\ge}5.1, we prove that the correlations have a power-law decay with distance along this entire phase.

A little statistical mechanics for the graph theorist

The random quantum q-state clock and Potts models are studied in two and three dimensions. The existence of Griffiths phases is tested in the two-dimensional case with q=6 by sampling the integrated probability distribution of local susceptibilities of the equivalent McCoy-Wu three-dimensional classical models with Monte Carlo simulations. For the random Potts model, numerical evidence of the existence of Griffiths phases is given and the finite-size effects are analyzed. For the clock model, the data also suggest the existence of a Griffiths phase but with much larger finite-size effects. The critical point of the random quantum clock model is then studied with the Strong-Disorder Renormalization Group. Evidence is given that, at strong enough disorder, this critical behavior is governed by the same infinite-disorder fixed point as the Potts model, for all the number of states q considered. At weak disorder, our renormalization group method becomes unstable and does not allow us to make conclusions.

The phase transitions and the thermodynamic properties of the two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a triangular lattice are studied on the base of the Wang–Landau algorithm of the Monte Carlo method. The phase transition characters are analyzed using the method of the four-order Binder cumulants and the histogram analysis of the data. It is found that a first-order phase transition is observed in the model under study.