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Finite-Size Scaling Analysis of a Three-Dimensional Blume–Capel Model in the Presence of External Magnetic Field

H Demirel, A. ÖZKAN, Bülent Kutlu

The Blume–Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent δ is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range −0.1 ≤ h = H/J ≤ 0. The estimated value of the field critical exponent δ is in good agreement with the universal value (δ = 5) in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.The Blume–Capel model in the presence of external magnetic field H has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton in three-dimension lattice. The field critical exponent δ is estimated using the power law relations and the finite size scaling functions for the magnetization and the susceptibility in the range −0.1 ≤ h = H/J ≤ 0. The estimated value of the field critical exponent δ is in good agreement with the universal value (δ = 5) in three dimensions. The simulations are carried out on a simple cubic lattice under periodic boundary conditions.

Chinese Physics LettersJul 1, 20081 citation

Scaling Laws for Dynamic Critical Phenomena

Wilhelm Brenig

Springer eBooksJan 1, 19890 citations

Scaling-Field Approach to Critical Phenomena

Eberhard K. Riedel, Kathie E. Newman

Springer series in solid-state sciencesJan 1, 19830 citations

Critical Points and Phase Transitions

Sergei M. Stishov, A. E. Petrova

Abstract Various critical phenomena and critical points appearing in many-particle systems under the variation of external conditions (fields), including the temperature, pressure, and magnetic and electric fields are described. Laws of statistical physics are universal for any particular nature of particles and the considered phenomena can be observed in systems of macroparticles (colloids), atoms, molecules, and subnuclear particles (nucleons and quarks).

Journal of Experimental and Theoretical PhysicsDec 1, 20209 citations

Scaling theory of the critical phenomena

Виктор Степанович Доценко

Cambridge University Press eBooksNov 2, 20000 citations

Dynamic Critical Phenomena in the Classical Approximation on a Lattice

Dominik Schweitzer, Justus Liebig University Giessen

The critical behaviour of a relativistic scalar field theory with Z2 symmetry is investigated near a second-order phase transition. Two sets of dynamic equations are employed, allowing to control conservation laws of both order parameter and energy density. We calculate spectral functions of the order parameter as well as unequal-time correlation functions of the energy momentum tensor at zero and non-vanishing spatial momenta from first-principles classical-statistical lattice simulations in real-time. For both, we investigate general properties and relevant degrees of freedom in distinct regions of the phase diagram. Close to the critical point, we find signatures of dynamic scaling behaviour and calculate the dynamic critical exponent z controlling the divergence of the critical time scale. For both the order parameter spectral function as well as the energy density autocorrelation, we extract universal dynamic scaling functions. Modifying the simulation framework to include dynamically changing temperature and external field allows us to study non-equilibrium phenomena. For the special case of instant quenches to the critical point, we identify universal scaling behaviour controlled by the initial magnetization, and calculate the related additional dynamic critical exponent. We extract the universal non-equilibrium scaling functions for the evolution of both the order parameter as well as the correlation length.The critical behaviour of a relativistic scalar field theory with Z2 symmetry is investigated near a second-order phase transition. Two sets of dynamic equations are employed, allowing to control conservation laws of both order parameter and energy density. We calculate spectral functions of the order parameter as well as unequal-time correlation functions of the energy momentum tensor at zero and non-vanishing spatial momenta from first-principles classical-statistical lattice simulations in real-time. For both, we investigate general properties and relevant degrees of freedom in distinct regions of the phase diagram. Close to the critical point, we find signatures of dynamic scaling behaviour and calculate the dynamic critical exponent z controlling the divergence of the critical time scale. For both the order parameter spectral function as well as the energy density autocorrelation, we extract universal dynamic scaling functions. Modifying the simulation framework to include dynamically changing temperature and external field allows us to study non-equilibrium phenomena. For the special case of instant quenches to the critical point, we identify universal scaling behaviour controlled by the initial magnetization, and calculate the related additional dynamic critical exponent. We extract the universal non-equilibrium scaling functions for the evolution of both the order parameter as well as the correlation length.

Jan 1, 20210 citations

Scaling laws and universality of critical phenomena in the presence of an external field

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