Sharp two- and three-dimensional phase transitional magnetization curves are obtained by an iterative renormalization-group coupling of Ising chains, which are solved exactly. The chains by themselves do not have a phase transition or nonzero magnetization, but the method reflects crossover from temperaturelike to fieldlike renormalization-group flows as the mechanism for the higher-dimensional phase transitions. The magnetization of each chain acts, via the interaction constant, as a magnetic field on its neighboring chains, thus entering its renormalization-group calculation. The method is highly flexible for wide application.Sharp two- and three-dimensional phase transitional magnetization curves are obtained by an iterative renormalization-group coupling of Ising chains, which are solved exactly. The chains by themselves do not have a phase transition or nonzero magnetization, but the method reflects crossover from temperaturelike to fieldlike renormalization-group flows as the mechanism for the higher-dimensional phase transitions. The magnetization of each chain acts, via the interaction constant, as a magnetic field on its neighboring chains, thus entering its renormalization-group calculation. The method is highly flexible for wide application.

arXiv:2006.05644Physical review. ESep 21, 20201 citation

Phase transitions in 1-D magnetic materials

E. V. Sannikov, R A Kozlitin, V. N. Udodov +1 more

Russian Physics JournalMar 1, 20061 citation

Quantum phase transitions in magnetic systems

Omid Nohadani

Jan 1, 20140 citations

Simulated tempering and magnetizing: Application of two-dimensional simulated tempering to the two-dimensional Ising model and its crossover

Tetsuro Nagai, Yuko Okamoto

We have performed two-dimensional simulated tempering (ST) simulations of the two-dimensional Ising model with different lattice sizes in order to investigate the two-dimensional ST's applicability to dealing with phase transitions and study the crossover of critical scaling behavior. The external field, as well as the temperature, was treated as a dynamical variable updated during the simulations. Thus this simulation can be referred to as simulated tempering and magnetizing (STM). We also performed simulated magnetizing (SM) simulations, in which the external field was considered as a dynamical variable and temperature was not. As discussed in previous studies, the ST method is not always compatible with first-order phase transitions. This is also true in the magnetizing process. Flipping of the entire magnetization did not occur in the SM simulations under the critical temperature T{c} in large-lattice-size simulations; however, the phase changed through the high-temperature region in the STM simulations. Thus the dimensional extension let us eliminate the difficulty of the first-order phase transitions and study a wide area of the phase space. We discuss how frequently parameter-updating attempts should be made for optimal convergence. The results favor frequent attempts. We finally study the crossover behavior of the phase transitions with respect to the temperature and external field. The crossover behavior is clearly observed in the simulations, in agreement with the theoretical implications.We have performed two-dimensional simulated tempering (ST) simulations of the two-dimensional Ising model with different lattice sizes in order to investigate the two-dimensional ST's applicability to dealing with phase transitions and study the crossover of critical scaling behavior. The external field, as well as the temperature, was treated as a dynamical variable updated during the simulations. Thus this simulation can be referred to as simulated tempering and magnetizing (STM). We also performed simulated magnetizing (SM) simulations, in which the external field was considered as a dynamical variable and temperature was not. As discussed in previous studies, the ST method is not always compatible with first-order phase transitions. This is also true in the magnetizing process. Flipping of the entire magnetization did not occur in the SM simulations under the critical temperature T{c} in large-lattice-size simulations; however, the phase changed through the high-temperature region in the STM simulations. Thus the dimensional extension let us eliminate the difficulty of the first-order phase transitions and study a wide area of the phase space. We discuss how frequently parameter-updating attempts should be made for optimal convergence. The results favor frequent attempts. We finally study the crossover behavior of the phase transitions with respect to the temperature and external field. The crossover behavior is clearly observed in the simulations, in agreement with the theoretical implications.

arXiv:1205.2523Physical Review ENov 9, 201212 citations

Computer simulation studies of magnetic phase transitions

D. P. Landau

Journal of Magnetism and Magnetic MaterialsOct 1, 199922 citations

Statistical properties of polarons in a magnetic field. II. Numerical results and discussion on the phase transition

François Maria Peeters, J. T. Devreese

A detailed numerical analysis is made of the analytic results presented in paper I. Numerical results are presented for the mass of the Feynman polaron, parallel (${M}_{\ensuremath{\parallel}}$) and perpendicular (${M}_{\ensuremath{\perp}}$) to the magnetic field, and for the following thermodynamic quantities: the magnetization, the susceptibility, the internal energy, the entropy, and the specific heat. Those quantities are studied for different values of the electron-phonon coupling ($\ensuremath{\alpha}$), temperature ( $T$ ), and magnetic field strength ( $\mathcal{H}$ ). We found that an ideal gas of polarons undergoes a phase transition. In the physical parameter space ($\frac{1}{\ensuremath{\alpha}},\frac{1}{\mathcal{H}},T$) the points of first-order phase transition define a two-dimensional surface which is circumscribed by a line of second-order phase transitions. At the transition point the polaron transforms in the direction perpendicular to the magnetic field, and with increasing magnetic field strength, from a polaron state (${M}_{\ensuremath{\parallel}}\ensuremath{\approx}{M}_{\ensuremath{\perp}}$) to an almost free Landau state (${M}_{\ensuremath{\parallel}}>>{M}_{\ensuremath{\perp}}\ensuremath{\sim}1$). This transition can be viewed as a magnetic-field-induced two-dimensional stripping of the polaron. The experimental consequences of this phase transition on the thermodynamic quantities and the magneto-optical absorption spectrum are discussed.A detailed numerical analysis is made of the analytic results presented in paper I. Numerical results are presented for the mass of the Feynman polaron, parallel (${M}_{\ensuremath{\parallel}}$) and perpendicular (${M}_{\ensuremath{\perp}}$) to the magnetic field, and for the following thermodynamic quantities: the magnetization, the susceptibility, the internal energy, the entropy, and the specific heat. Those quantities are studied for different values of the electron-phonon coupling ($\ensuremath{\alpha}$), temperature ($T$), and magnetic field strength ($\mathcal{H}$). We found that an ideal gas of polarons undergoes a phase transition. In the physical parameter space ($\frac{1}{\ensuremath{\alpha}},\frac{1}{\mathcal{H}},T$) the points of first-order phase transition define a two-dimensional surface which is circumscribed by a line of second-order phase transitions. At the transition point the polaron transforms in the direction perpendicular to the magnetic field, and with increasing magnetic field strength, from a polaron state (${M}_{\ensuremath{\parallel}}\ensuremath{\approx}{M}_{\ensuremath{\perp}}$) to an almost free Landau state (${M}_{\ensuremath{\parallel}}>>{M}_{\ensuremath{\perp}}\ensuremath{\sim}1$). This transition can be viewed as a magnetic-field-induced two-dimensional stripping of the polaron. The experimental consequences of this phase transition on the thermodynamic quantities and the magneto-optical absorption spectrum are discussed.

Physical review. B, Condensed matterJun 15, 198258 citations

T

), and magnetic field strength (

\mathcal{H}

). We found that an ideal gas of polarons undergoes a phase transition. In the physical parameter space ($\frac{1}{\ensuremath{\alpha}},\frac{1}{\mathcal{H}},T$) the points of first-order phase transition define a two-dimensional surface which is circumscribed by a line of second-order phase transitions. At the transition point the polaron transforms in the direction perpendicular to the magnetic field, and with increasing magnetic field strength, from a polaron state (${M}_{\ensuremath{\parallel}}\ensuremath{\approx}{M}_{\ensuremath{\perp}}$) to an almost free Landau state (${M}_{\ensuremath{\parallel}}>>{M}_{\ensuremath{\perp}}\ensuremath{\sim}1$). This transition can be viewed as a magnetic-field-induced two-dimensional stripping of the polaron. The experimental consequences of this phase transition on the thermodynamic quantities and the magneto-optical absorption spectrum are discussed.