Number Of Spin States Research Articles

Antiferromagnitnaya model' Pottsa na ob\"emno-tsentrirovannoy kubicheskoy reshetke

We have studied phase transitions and thermodynamic properties of the antiferromagnetic Potts model with number of spin states q = 3 on a body-centered cubic lattice by the Monte Carlo method. Investigations have been performed with account for exchange interactions J1 and J2 between the first and second nearest neighbors. The phase transition order has been analyzed using the histogram method. It is found that in this model with J2 = 0, a second-order phase transition is observed. It is concluded that the inclusion of the interaction between the second nearest neighbors changes the type of the phase transition.

A general method for locating stationary points on the mixed-spin surface of spin-forbidden reaction with multiple spin states.

Some chemical reactions proceed on multiple potential energy surfaces and are often accompanied by a change in spin multiplicity, being called spin-forbidden reactions, where the spin-orbit coupling (SOC) effects play a crucial role. In order to efficiently investigate spin-forbidden reactions with two spin states, Yang et al. [Phys. Chem. Chem. Phys. 20, 4129-4136 (2018)] proposed a two-state spin-mixing (TSSM) model, where the SOC effects between the two spin states are simulated by a geometry-independent constant. Inspired by the TSSM model, we suggest a multiple-state spin-mixing (MSSM) model in this paper for the general case with any number of spin states, and its analytic first and second derivatives have been developed for locating stationary points on the mixed-spin potential energy surface and estimating thermochemical energies. To demonstrate the performance of the MSSM model, some spin-forbidden reactions involving 5d transition elements are calculated using the density functional theory (DFT), and the results are compared with the two-component relativistic ones. It is found that MSSM DFT and two-component DFT calculations may provide very similar stationary-point information on the lowest mixed-spin/spinor energy surface, including structures, vibrational frequencies, and zero-point energies. For the reactions containing saturated 5d elements, the reaction energies by MSSM DFT and two-component DFT agree very well within 3 kcal/mol. As for the two reactions OsO+ + CH4 → OOs(CH2)+ + H2 and W + CH4 → WCH2 + H2 involving unsaturated 5d elements, MSSM DFT may also yield good reaction energies of similar accuracy but with some counterexamples. Nevertheless, the energies may be remarkably improved by a posteriori single point energy calculations using two-component DFT at the MSSM DFT optimized geometries, and the maximum error of about 1 kcal/mol is almost independent of the SOC constant used. The MSSM method as well as the developed computer program provides an effective utility for studying spin-forbidden reactions.

Phase Transitions in a Frustrated Four-Vertex Potts Model on a Hexagonal Lattice in a Magnetic Field

The effect of a magnetic field on the phase transitions of a two-dimensional frustrated Potts model with the number of spin states q = 4 on a hexagonal lattice was studied by the Monte Carlo method. The studies were carried out for a wide range of magnetic field strength. The magnetic structures of the ground state in this range have been obtained. The dependence of the magnetization on the magnetic field has been constructed. It has been found that an external magnetic field leads to a first-order phase transition. It is shown that a strong magnetic field removes the degeneracy of the ground state and suppresses the phase transition in the system

Энергетический анализ магнитных структур основного состояния модели Поттса

Based on the Wang-Landau algorithm, the Monte Carlo method was used to perform an energy analysis of the magnetic structures of the ground state of the two-dimensional Potts model with the number of spin states $q=4$ on a triangular lattice, taking into account the exchange interactions of the first $J_1$ and second $J_2$ nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the interval $-2.0 \leq J_2 \leq 0.0$. The magnetic structures of the ground state are determined for different values of the interaction of the second nearest neighbors. It is found that a change in the magnitude of the interaction of the second nearest neighbors in this model leads to a change in the magnetic ordering.

Frustrated Potts Model with Number of Spin States q = 4 in Magnetic Field

Frustrated Potts Model with Number of Spin States q = 4 in Magnetic Field

Phase Transitions in the Diluted Two-Dimensional Potts Model with the Number of Spin States q = 3 on a Square Lattice

Phase Transitions in the Diluted Two-Dimensional Potts Model with the Number of Spin States q = 3 on a Square Lattice

Studying the Effect of Strong Magnetic Fields on the Phase Transitions of the Frustrated Potts Model with a Number of Spin States q = 4

Studying the Effect of Strong Magnetic Fields on the Phase Transitions of the Frustrated Potts Model with a Number of Spin States q = 4

Investigation of the influence of weak magnetic fields on thermodynamic properties of the Potts model with the number of spin states q=4 on a hexagonal lattice

The replica exchange algorithm of the Monte Carlo method was used to study phase transitions and thermodynamic properties of the two-dimensional Potts model with the number of spin states q=4 on a hexagonal lattice in weak magnetic fields. The studies were carried out for the interval of the magnetic field value 0.0≤ H≤3.0 with a step of 1.0. It is found that a first-order phase transition is observed in the considered range of field values. Keywords: Frustration, Phase transitions, Monte Carlo method, Potts model.

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

The phase transitions and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with the number of spin states q=4 on the kagome lattice are studied by the Monte Carlo method, taking into account the exchange interactions of the first J1 and second J2 nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the interval -1.0≤ J_2≤0.0. An analysis of the character of phase transitions has been carried out. It is shown that in the interval -1.0≤ J_2≤-0.1, a second-order phase transition is observed, while at J_2=0.0, frustrations disturb the order in the system and lead to the disappearance of the phase transition Keywords: Frustration, phase transition, Monte Carlo method, Potts model.

Energy analysis of magnetic structures of the ground state of the Potts model with competing exchange interactions

Based on the Wang--Landau algorithm, the Monte Carlo method was used to study the magnetic structures of the ground state and the thermodynamic properties of the two-dimensional Potts model with the number of spin states q=4 on a triangular lattice, taking into account the exchange interactions of the first J1 and second J2 nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the range -2.0≤ J2≤0.0. The magnetic structures of the ground state are constructed in the interval considered. An energy analysis of the magnetic structures of the ground state has been carried out. A phase diagram of the dependence of the critical temperature on the value of J2 is constructed. It is shown that taking into account the interactions of the second nearest neighbors leads to the appearance of frustrations and violation of the magnetic ordering. Keywords: Frustrations, magnetic structures, Monte Carlo method, Potts model.

Исследование влияния слабых магнитных полей на термодинамические свойства модели Поттса с числом состояний спина q=4 на гексагональной решетке

The replica exchange algorithm of the Monte Carlo method was used to study phase transitions and thermodynamic properties of the two-dimensional Potts model with the number of spin states q = 4 on a hexagonal lattice in weak magnetic fields. The studies were carried out for the interval of the magnetic field value 0.0 ≤ Н ≤ 3.0 with a step of 1.0. It is found that a first-order phase transition is observed in the considered range of field values.

Энергетический анализ магнитных структур основного состояния модели Поттса с конкурирующими обменными взаимодействиями

Based on the Wang-Landau algorithm, the Monte Carlo method was used to study the magnetic structures of the ground state and the thermodynamic properties of the two-dimensional Potts model with the number of spin states q=4 on a triangular lattice, taking into account the exchange interactions of the first J1 and second J2 nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the range -2.0≤ J2≤0.0. The magnetic structures of the ground state are constructed in the interval considered. An energy analysis of the magnetic structures of the ground state has been carried out. A phase diagram of the dependence of the critical temperature on the value of J2 is constructed. It is shown that taking into account the interactions of the second nearest neighbors leads to the appearance of frustrations and violation of the magnetic ordering.

Фазовые переходы в двумерной антиферромагнитной модели Поттса на решетке кагоме

The phase transitions and thermodynamic properties of the two-dimensional antiferromagnetic Potts model with the number of spin states q = 4 on the kagome lattice are studied by the Monte Carlo method, taking into account the exchange interactions of the first J1 and second J2 nearest neighbors. The studies were carried out for the value of the interaction of the second nearest neighbors in the interval -1.0 ≤ J2 ≤ 0.0. An analysis of the character of phase transitions has been carried out. It is shown that in the interval -1.0 ≤ J2 ≤ -0.1, a second-order phase transition is observed, while at J2 = 0.0, frustrations disturb the order in the system and lead to the disappearance of the phase transition.

Компьютерное моделирование двумерной модели Поттса с конкурирующими обменными взаимодействиями

The phase transitions and thermodynamic properties of the two-dimensional Potts model with the number of spin states $q = 4$ on a hexagonal lattice with competing exchange interactions have been investigated on the basis of the Wang-Landau algorithm by the Monte Carlo method. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbors leads to a violation of the magnetic ordering and to the appearance of frustration.

Гистограммный анализ данных для трехмерной слабо разбавленной модели Поттса с числом состояний спина q = 5

Гистограммный анализ данных для трехмерной слабо разбавленной модели Поттса с числом состояний спина q = 5

Phase diagram of the Potts model with the number of spin states q = 4 on a kagome lattice

The magnetic structures of the ground state, phase transitions, and the thermodynamic properties of a two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a kagome lattice are studied using the Wang-Landau algorithm of the Monte Carlo method, taking into account the interactions of the nearest and the next-nearest neighbors. The studies were carried out for the value of the interaction of the next-nearest neighbors in the range 0 ≤ r ≤ 1.0. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbor leads to a violation of the magnetic ordering. A phase diagram of the dependence of the critical temperature on the value of the interaction of the next-nearest neighbor is constructed. The analysis of the character of phase transitions is carried out. It was found that in the ranges 0 ≤ r ≤ 0.5 and 0.5 ≤ r ≤ 1.0, a first-order phase transition is observed, and for r = 0.5, frustrations are observed in the system.

Phase Diagram of the Potts Model with the Number of Spin States q = 4 on a Hexagonal Lattice

Phase Diagram of the Potts Model with the Number of Spin States q = 4 on a Hexagonal Lattice

Calculation of relative dispersions of magnetization, susceptibility, and heat capacity in a two-dimensional weakly diluted Potts model based on computer simulation methods

The Monte Carlo method was used to calculate the relative dispersions of the magnetization Rm, susceptibility Rχ, and heat capacity RC for a weakly diluted impurity Potts model with the number of spin states q = 4. It is shown that the introduction of disorder in the form of nonmagnetic impurities into the two-dimensional Potts model with q = 4 on square lattice leads to nonzero values for Rm, Rχ, and RC at the critical point.

Phase Transitions and the Thermodynamic Properties of the Potts Model with the Spin State Number q = 4 at a Kagome Lattice

Phase transitions and the thermodynamic properties of the two-dimensional ferromagnetic Izing model with spin state number q = 4 on a kagome lattice are studied by the Monte Carlo method on the base of the Wang–Landau algorithm. The phase transition character is analyzed using the fourth-order Binder cumulant method and the histogram analysis of the data. It is found that this model undergoes a first-order phase transition.

Production of ^4mathrm{Li} and p!-!^3mathrm{He} correlation function in relativistic heavy-ion collisions

The thermal and coalescence models both describe well yields of light nuclei produced in relativistic heavy-ion collisions at LHC. We propose to measure the yield of ^4mathrm{Li} and compare it to that of ^4mathrm{He} to falsify one of the models. Since the masses of ^4mathrm{He} and ^4mathrm{Li} are almost equal, the yield of ^4mathrm{Li} is about 5 times bigger than that of ^4mathrm{He} in the thermal model because of different numbers of spin states of the two nuclides. Their internal structures are, however, very different: the alpha particle is well bound and compact while ^4mathrm{Li} is weakly bound and loose. Consequently, the ratio of yields of ^4mathrm{Li} to ^4mathrm{He} is significantly smaller in the coalescence model and it strongly depends on the collision centrality. Since the nuclide ^4mathrm{Li} is unstable and it decays into ^3mathrm{He} and p, the yield of ^4mathrm{Li} can be experimentally obtained through a measurement of the p!-!^3mathrm{He} correlation function. The function carries information not only about the yield of ^4mathrm{Li} but also about the source of ^3mathrm{He} and allows one to determine through a source-size measurement whether of ^3mathrm{He} is directly emitted from the fireball or it is formed afterwards. We compute the correlation function taking into account the s-wave scattering and Coulomb repulsion together with the resonance interaction responsible for the ^4mathrm{Li} nuclide. We discuss how to infer information about an origin of ^3mathrm{He} from the correlation function, and finally a method to obtain the yield of ^4mathrm{Li} is proposed.