Non-Equilibrium Critical Dynamics of Ferromagnets with Long Range Correlated Defects

2012 ◽  
Vol 190 ◽  
pp. 31-34
Author(s):  
Dmitry N. Kulikov ◽  
Pavel V. Prudnikov
Keyword(s):  
Critical Exponent ◽  
Long Range ◽  
Critical Behavior ◽  
Disordered Systems ◽  
Asymptotic Series ◽  
Three Dimensional ◽  
Time Regime ◽  
Short Time ◽  
Short Time Evolution ◽  
Non Equilibrium

The simultaneous effect of non-equilibrium initial states and correlation betweendefects of the structure on the evolution of anisotropic disordered systems at the critical pointwas analyzed. The field theory description of the non-equilibrium critical behavior of three-dimensional disordered systems with the long-range correlated defects was given and the dy-namical critical exponent of the short-time evolution was calculated in the two-loop approxima-tion without the use of the "-expansion. The values of the dynamical critical exponent obtainedby using various methods for summing asymptotic series were compared with the results ofthe computer simulation of the non-equilibrium critical behavior of the three-dimensional dis-ordered Ising model in the short-time regime.

Non-Equilibrium Critical Relaxation of Heisenberg Ferromagnets with Long-Range Correlated Defects

2012 ◽  
Vol 190 ◽  
pp. 39-42
Author(s):  
M. Medvedeva ◽  
Pavel V. Prudnikov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Initial State ◽  
Short Time ◽  
Theoretic Description ◽  
Good Agreement

The dynamic critical behavior of the three-dimensional Heisenberg model with longrangecorrelated disorder was studied by using short-time Monte Carlo simulations at criticality.The static and dynamic critical exponents are determined. The simulation was performed fromordered initial state. The obtained values of the exponents are in a good agreement with resultsof the field-theoretic description of the critical behavior of this model in the two-loopapproximation.

Short-time dynamics and critical behavior of three-dimensional bond-diluted Potts model

2006 ◽  
Vol 49 (2) ◽  
pp. 195-203 ◽  
Author(s):  
J. Q. Yin ◽  
B. Zheng ◽  
V. V. Prudnikov ◽  
S. Trimper
Keyword(s):  
Critical Behavior ◽  
Potts Model ◽  
Three Dimensional ◽  
Time Dynamics ◽  
Short Time

Critical behavior of a 3D Ising-like system in the higher non-Gaussian approximation: Inclusion of the critical exponent of the correlation function

2014 ◽  
Vol 28 (24) ◽  
pp. 1450160 ◽  
Author(s):  
I. R. Yukhnovskii ◽  
M. P. Kozlovskii ◽  
I. V. Pylyuk
Keyword(s):  
Correlation Function ◽  
Critical Exponent ◽  
Critical Behavior ◽  
Gaussian Approximation ◽  
Three Dimensional ◽  
Universality Class ◽  
Spin Moment ◽  
Collective Variables ◽  
Function Calculation ◽  
Non Gaussian

A microscopic description of the critical behavior of systems belonging to the universality class of the three-dimensional (3D) Ising model is developed within the collective variables (CV) approach. The higher non-Gaussian approximation (the sextic distribution for the modes of spin-moment density oscillations or the ρ6 model) is used. A specific feature of the partition function calculation for an Ising-like system is the inclusion of the correction for the potential averaging. This correction leads to the modified recurrence relations (RR) for the ρ6 model and a nonzero critical exponent of the correlation function η. The RR between the coefficients of the effective sextic distributions are written and analyzed. A technique for determining the small critical exponent η is elaborated in the higher non-Gaussian approximation. It is shown that the renormalized critical exponent of the correlation length has a tendency to a reduction in the case when the exponent η is taken into account.

scholarly journals Critical Behaviour in Systems in which Long-Range and Short-Range Forces Compete

2019 ◽  
pp. 37-47 ◽  
Author(s):  
S.V. Belim
Keyword(s):  
Critical Exponent ◽  
Long Range ◽  
Critical Exponents ◽  
Short Range ◽  
Asymptotic Series ◽  
Critical Behaviour ◽  
Interaction Parameters ◽  
Theory Approach ◽  
Range Interaction ◽  
Long Range Interaction

Critical behaviour of a range of ferromagnetic materials deviates from the predictions of the Ising, XY and Heisenberg models. Additional long-range forces competing with regular exchange interaction may explain this deviation. These competing interactions lead to new universality classes of critical behaviour. The paper uses the field theory approach to investigate critical behaviour in those systems in which long-range and short-range forces compete. We consider the case when a power function of distance r-D-σ, when 1.5 < σ < 2.0, can describe the long-range forces. There exists a distinctive critical behaviour mode for these values. We derived vertex functions using a two-loop approximation directly in three-dimensional space (D = 3) and, for all values, obtained a linear approximation of asymptotic series in terms of long-range interaction parameters. We applied the Pade --- Borel summation technique to these asymptotic series. We computed stable fixed points and critical exponents as functions of long-range interaction parameters for low relativeefficiency of the long-range interaction. We investigated how critical exponents depend on the factor in the power law and relative long-range interaction intensity. We compared our results to the critical exponent values found experimentally for manganites. We used the experimental critical exponent γ values to compute long-range interaction parameters and then used the long-range interaction parameters to derive the ß exponent values, which we then compared to the experimental values. We show good agreement between our theoretical results and experimental data.

scholarly journals SHORT-TIME RELAXATION OF SU(2) LATTICE GAUGE THEORY IN (3 + 1) DIMENSIONS

2000 ◽  
Vol 11 (07) ◽  
pp. 1465-1474 ◽  
Author(s):  
A. JASTER
Keyword(s):  
Gauge Theory ◽  
Lattice Gauge Theory ◽  
Three Dimensional ◽  
Polyakov Loop ◽  
Monte Carlo Algorithm ◽  
Dynamic Relaxation ◽  
Lattice Gauge ◽  
Time Regime ◽  
Short Time ◽  
Ordered State

We investigate the dynamic relaxation for SU(2) gauge theory at finite temperatures in (3 + 1) dimensions. Using the Hybrid Monte Carlo algorithm, we examine the time dependence of the system in the short-time regime. Starting from the ordered state, the critical exponents β, ν and z are calculated from the power law behavior of the Polyakov loop and the cumulant at or near the critical point. The results for the static exponents are in agreement with those obtained from simulations in equilibrium and those of the three-dimensional Ising model. The value for the dynamic critical exponent was determined with z = 2.0(1).

scholarly journals Short-time dynamics and critical behavior of the three-dimensional site-diluted Ising model

2010 ◽  
Vol 81 (1) ◽  
Author(s):  
Vladimir V. Prudnikov ◽  
Pavel V. Prudnikov ◽  
Aleksandr S. Krinitsyn ◽  
Andrei N. Vakilov ◽  
Evgenii A. Pospelov ◽  
...  
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Three Dimensional ◽  
Time Dynamics ◽  
Short Time
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