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Известия Алтайского государственного университета

Особенности поведения теплоемкости в одномерных магнетиках, описываемых моделью Изинга

E. V. Shabunina, D.V. Spirin, Удодов Владимир Николаевич

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

The temperature dependences of a specific heat and a critical exponent α of a specific heat is investigated by means of Monte Carlo simulations for Ising model magnetic, taking into account the interactions in the second and third coordination spheres. Universality of index α for the various sizes of chains is proved. It is established that the critical exponent α significantly depends on energy of interaction in the second and third coordination spheres.

Related papers

Influence of the interaction on the heat capacity critical exponent for 1D Ising ferromagnet with periodical boundary conditions

Zh. V. Dzyuba, V. N. Udodov, D.V. Spirin

In the framework of the spin flip dynamics algorithm with an original expression for the energy, an influence of the interaction of second, third neighbors, four-particle interaction, temperature and size of a 1D Ising ferromagnet on the heat capacity critical exponent is studied. Periodic border conditions are used. The critical index α is calculated by the finite size scaling method. It is established that the growth of energy parameters of the multi-spin interaction significantly affects the heat capacity exponent. Interaction energy of third neighbors decreases the value of α to a greater extent than the second-neighbor interaction J2 and four-particle one J1 – 4. Different characters of the influence of pair and four-particle interactions on α are revealed. Energy parameters are established for which this critical exponent attains negative values. For instance, taking into account the interaction energy of third neighbors, with an approach to the critical region, the heat capacity critical exponent has a minimum near negative value of α = –0.0043 ± 0.0005. With increasing number of nodes in the 1D Ising chain, heat capacity critical exponent increases. Extrapolation according to the inverse size of the system in the thermodynamic limit gives the values α = 0.19 ± 0.02, α = 0.17 ± 0.02, α = 0.20 ± 0.02, when one takes into account the interaction energy of second neighbors J2 = 0.1, third neighbors J3 = 0.1 and four-particle interaction J1 – 4 = 0.1, respectively. Note that the second neighbor and four-particle interaction energies do not change the sign of the critical exponent for N > 6, and when approaching the critical region the critical exponent α tends to zero. The results obtained are compared with the values for Ising model with "broken ends" boundary conditions, as well as with other known results for two-dimensional and three-dimensional cases.

Letters on Materials•Jan 1, 2017•1 citation

Критические свойства в модели Изинга на треугольной решетке с переменным межслойным обменным взаимодействием

Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

The Monte Carlo replica algorithm studies of phase transitions and critical phenomenaofthe layered triangular antiferromagnetic Ising model withvariable interlayer exchange interaction. Investigations were carried out for the ratios of the value of the intralayerJ1 and interlayer J2 exchange interactions in the range of values r = J2 / J1 = 0.01 ÷ 1.0. It was found that in the above range r is observed second-order phase transition.Static critical exponents for the heat capacityα, susceptibility γ, order parameter β, correlation radius ν, and the Fisher exponent ηare computed by means of the finite-size scaling theory. It is shown that the universality class of the critical behavior of the model is maintained in the range of 0.05 <r≤1.0.The results obtained suggest that3D frustrated Ising models on stacked triangularlattice with interlayer-to-intralayer exchange ratio 0.05<r≤1.0. preserves the universality class of criticalbehavior. At lower r, a crossover from 3D to 2D criticalbehavior is observed.

Physics of the Solid State•Jan 1, 2019•0 citations

Фазовые переходы в фрустрированных моделях Изинга (О б з о р)

А.К. Муртазаев, М.К. Рамазанов

The current state of research on phase transitions and critical phenomena in frustration is considered. modeled Ising models. The results obtained on the basis of highly efficient algorithms are discussed. Monte Carlo method for Ising models on lattices of various dimensions and types. A main attention given to the results of studying phase transitions, critical and thermodynamic properties of models Ising, taking into account the exchange interactions of the first and second neighbors, as well as the external magnetic fields. Phase diagrams of the dependence of the critical temperature on the value of the exchange interactions of second neighbors and an external magnetic field. The regions of observation of phase transitions of the first and second kind. The universality classes of critical behavior are established. For some models have ranges with non-universal critical behavior. Discussed features of the critical behavior of frustrated Ising models.

Physics of the Solid State•Jan 1, 2023•2 citations

Компьютерное моделирование критического поведения трехмерной неупорядоченной модели Изинга

В. Н. Бородихин, Andrey N. Vakilov, Vladimir V. Prudnikov +1 more

Using Monte Carlo simulations it was studied the three-dimensional site-diluted Ising model in a wide dilution range. The scaling functions and values of exponents for susceptibility and correlation length were determined with the use of finite size scaling method. They demonstrate the existence two classes of universal critical behavior of diluted Ising systems with different characteristics for weakly and highly disordered systems.

Matematičeskie struktury i modelirovanie•Jan 1, 2003•0 citations

Monte Carlo simulation of strongly disordered Ising ferromagnets

Hans-Otto Heuer

We report extensive Monte Carlo simulations of disordered Ising systems in the ferromagnetic region with concentrations of magnetic sites between p=1.0 and 0.5. The magnetization, the susceptibility, and the caloric properties have been studied in the critical region. The critical exponents \ensuremath{\beta} and \ensuremath{\gamma} as well as the universal amplitude A of the magnetization and the ratio ${\mathit{C}}_{+}$/${\mathit{C}}_{\mathrm{\ensuremath{-}}}$ of the susceptibility amplitudes have been determined with high precision. In addition to the cusplike specific heat, we have also measured the magnetization-energy correlation function \ensuremath{\Gamma}, which is a divergent thermal quantity. The corresponding critical exponent \ensuremath{\zeta}, which is related to the other exponents by \ensuremath{\zeta}=1-\ensuremath{\beta}=(\ensuremath{\alpha}+\ensuremath{\gamma})/2, has been determined. We have found that all quantities show power-law behavior within the temperature range of our simulation. All critical exponents change continuously with dilution. Even in the range of weak dilution (p\ensuremath{\ge}0.8), the effective critical exponents are concentration dependent and are clearly different from their pure system values. In the strongly diluted regime the critical exponents gradually reach new asymptotic behavior at p=0.5--0.6 with values of \ensuremath{\beta}=0.335\ifmmode\pm\else\textpm\fi{}0.01 and \ensuremath{\gamma}=1.49\ifmmode\pm\else\textpm\fi{}0.02. The exponent \ensuremath{\alpha} of the specific heat becomes -0.17\ifmmode\pm\else\textpm\fi{}0.04, which corresponds to a cusplike singularity. We conclude that disorder profoundly changes the critical behavior for weakly as well as strongly disordered spin systems.

Physical review. B, Condensed matter•Oct 1, 1990•55 citations

Критический индекс восприимчивости 1D-изинговского ферромагнетика, замкнутого в кольцо

Zh. V. Dzyuba, Удодов Владимир Николаевич

AbstractUsing the Monte Carlo method, critical behavior of the one-dimensional ferromagnetic Ising model has been investigated with allowance for the interaction of the second and third neighbors and four-particle interaction. The obtained results on the critical temperature were compared with the critical temperature of the quasi-one-dimensional Ising magnetic [(СН_3)_3NH] · FeCl_3 · 2H_2O and with the magnitude of the exchange interaction J/k _B = 17.4 K. Within the scope of the finite-dimensional scaling theory, the critical susceptibility exponent has been calculated. It has been shown that values of the susceptibility exponent for the one-dimensional Ising model with periodic boundary conditions are considerably less than the known values of the exponents for three-dimensional systems. The critical susceptibility exponent strongly depends on energy parameters; namely, it decreases with an increase in them.

Physics of the Solid State•Jan 1, 2018•1 citation
The temperature dependences of a specific heat and a critical exponent α of a specific heat is investigated by means of Monte Carlo simulations for Ising model magnetic, taking into account the interactions in the second and third coordination spheres. Universality of index α for the various sizes of chains is proved. It is established that the critical exponent α significantly depends on energy of interaction in the second and third coordination spheres.
In the framework of the spin flip dynamics algorithm with an original expression for the energy, an influence of the interaction of second, third neighbors, four-particle interaction, temperature and size of a 1D Ising ferromagnet on the heat capacity critical exponent is studied. Periodic border conditions are used. The critical index α is calculated by the finite size scaling method. It is established that the growth of energy parameters of the multi-spin interaction significantly affects the heat capacity exponent. Interaction energy of third neighbors decreases the value of α to a greater extent than the second-neighbor interaction J2 and four-particle one J1 – 4. Different characters of the influence of pair and four-particle interactions on α are revealed. Energy parameters are established for which this critical exponent attains negative values. For instance, taking into account the interaction energy of third neighbors, with an approach to the critical region, the heat capacity critical exponent has a minimum near negative value of α = –0.0043 ± 0.0005. With increasing number of nodes in the 1D Ising chain, heat capacity critical exponent increases. Extrapolation according to the inverse size of the system in the thermodynamic limit gives the values α = 0.19 ± 0.02, α = 0.17 ± 0.02, α = 0.20 ± 0.02, when one takes into account the interaction energy of second neighbors J2 = 0.1, third neighbors J3 = 0.1 and four-particle interaction J1 – 4 = 0.1, respectively. Note that the second neighbor and four-particle interaction energies do not change the sign of the critical exponent for N > 6, and when approaching the critical region the critical exponent α tends to zero. The results obtained are compared with the values for Ising model with "broken ends" boundary conditions, as well as with other known results for two-dimensional and three-dimensional cases.
The Monte Carlo replica algorithm studies of phase transitions and critical phenomenaofthe layered triangular antiferromagnetic Ising model withvariable interlayer exchange interaction. Investigations were carried out for the ratios of the value of the intralayerJ1 and interlayer J2 exchange interactions in the range of values r = J2 / J1 = 0.01 ÷ 1.0. It was found that in the above range r is observed second-order phase transition.Static critical exponents for the heat capacityα, susceptibility γ, order parameter β, correlation radius ν, and the Fisher exponent ηare computed by means of the finite-size scaling theory. It is shown that the universality class of the critical behavior of the model is maintained in the range of 0.05 <r≤1.0.The results obtained suggest that3D frustrated Ising models on stacked triangularlattice with interlayer-to-intralayer exchange ratio 0.05<r≤1.0. preserves the universality class of criticalbehavior. At lower r, a crossover from 3D to 2D criticalbehavior is observed.
The current state of research on phase transitions and critical phenomena in frustration is considered. modeled Ising models. The results obtained on the basis of highly efficient algorithms are discussed. Monte Carlo method for Ising models on lattices of various dimensions and types. A main attention given to the results of studying phase transitions, critical and thermodynamic properties of models Ising, taking into account the exchange interactions of the first and second neighbors, as well as the external magnetic fields. Phase diagrams of the dependence of the critical temperature on the value of the exchange interactions of second neighbors and an external magnetic field. The regions of observation of phase transitions of the first and second kind. The universality classes of critical behavior are established. For some models have ranges with non-universal critical behavior. Discussed features of the critical behavior of frustrated Ising models.
We report extensive Monte Carlo simulations of disordered Ising systems in the ferromagnetic region with concentrations of magnetic sites between p=1.0 and 0.5. The magnetization, the susceptibility, and the caloric properties have been studied in the critical region. The critical exponents \ensuremath{\beta} and \ensuremath{\gamma} as well as the universal amplitude A of the magnetization and the ratio C+{\mathit{C}}_{+}C+​/${\mathit{C}}_{\mathrm{\ensuremath{-}}}$ of the susceptibility amplitudes have been determined with high precision. In addition to the cusplike specific heat, we have also measured the magnetization-energy correlation function \ensuremath{\Gamma}, which is a divergent thermal quantity. The corresponding critical exponent \ensuremath{\zeta}, which is related to the other exponents by \ensuremath{\zeta}=1-\ensuremath{\beta}=(\ensuremath{\alpha}+\ensuremath{\gamma})/2, has been determined. We have found that all quantities show power-law behavior within the temperature range of our simulation. All critical exponents change continuously with dilution. Even in the range of weak dilution (p\ensuremath{\ge}0.8), the effective critical exponents are concentration dependent and are clearly different from their pure system values. In the strongly diluted regime the critical exponents gradually reach new asymptotic behavior at p=0.5--0.6 with values of \ensuremath{\beta}=0.335\ifmmode\pm\else\textpm\fi{}0.01 and \ensuremath{\gamma}=1.49\ifmmode\pm\else\textpm\fi{}0.02. The exponent \ensuremath{\alpha} of the specific heat becomes -0.17\ifmmode\pm\else\textpm\fi{}0.04, which corresponds to a cusplike singularity. We conclude that disorder profoundly changes the critical behavior for weakly as well as strongly disordered spin systems.
AbstractUsing the Monte Carlo method, critical behavior of the one-dimensional ferromagnetic Ising model has been investigated with allowance for the interaction of the second and third neighbors and four-particle interaction. The obtained results on the critical temperature were compared with the critical temperature of the quasi-one-dimensional Ising magnetic [(СН_3)_3NH] · FeCl_3 · 2H_2O and with the magnitude of the exchange interaction J/k _B = 17.4 K. Within the scope of the finite-dimensional scaling theory, the critical susceptibility exponent has been calculated. It has been shown that values of the susceptibility exponent for the one-dimensional Ising model with periodic boundary conditions are considerably less than the known values of the exponents for three-dimensional systems. The critical susceptibility exponent strongly depends on energy parameters; namely, it decreases with an increase in them.