PHASE TRANSITION IN CONTINUOUS SYMMETRY MODEL IN GENERAL DIMENSIONS — FIXED DIMENSION RENORMALIZATION GROUP APPROACH

1993 ◽  
Vol 08 (30) ◽  
pp. 5329-5351 ◽  
Author(s):  
YU. HOLOVATCH
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Symmetric Model ◽  
Continuous Symmetry ◽  
Group Approach ◽  
Fixed Dimension ◽  
Loop Approximation ◽  
Renormalization Group Approach ◽  
Borel Transformation ◽  
Group Functions

Critical exponents of the O(m)-symmetric model are calculated in the case when dimension of space is noninteger. Calculations are performed in the frames of the field-theoretical approach using the three-loop approximation. Renormalization group functions in the Callan-Symanzik scheme are considered directly in noninteger dimensions. Perturbation theory expansions are resummed with the use of Padé-Borel transformation.

Field-Theory Description of Nonequilibrium Critical Dynamics for Spin Systems

2012 ◽  
Vol 190 ◽  
pp. 23-26
Author(s):  
Ivan A. Kalashnikov ◽  
Pavel V. Prudnikov
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Order Parameter ◽  
Spin Systems ◽  
Critical Dynamics ◽  
Relaxation Dynamics ◽  
Group Approach ◽  
Fixed Dimension ◽  
Renormalization Group Approach ◽  
Short Time

Renormalization-group approach is applied to investigate the short-time nonequilibriumcritical behavior of pure and diluted spin systems with nonmagnetic point-like impurities.The dissipative relaxation dynamics with non-conserved order parameter is considered. For thefirst time the description of the order parameter growth induced by the initial nonequilibriumstate of system is carried out at fixed dimension d = 3 without use of ε-expansion.

scholarly journals AN EXACT RENORMALIZATION GROUP APPROACH TO FRUSTRATED MAGNETS

2001 ◽  
Vol 16 (11) ◽  
pp. 2131-2136 ◽  
Author(s):  
M. TISSIER ◽  
B. DELAMOTTE ◽  
D. MOUHANNA
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Frustrated Magnets ◽  
Group Approach ◽  
Perturbative Methods ◽  
Renormalization Group Approach ◽  
Exact Renormalization Group ◽  
Coherent Picture ◽  
Apparent Conflict ◽  
Good Agreement

Frustrated magnets are a notorious example where usual perturbative methods fail. Having recourse to an exact renormalization group approach, one gets a coherent picture of the physics of Heisenberg frustrated magnets everywhere between d=2 and d=4: all known perturbative results are recovered in a single framework, their apparent conflict is explained while the description of the phase transition in d=3 is found to be in good agreement with the experimental context.

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