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Applying thermal renormalization group (TRG) equations to $\phi^4$ theorywith spontaneous breaking symmetry, we investigate the critical behavior of thedamping rate for the plasmons with finite momentum at the symmetry-restoringphase transition. From the TRG equation the IR cutoff provided by the externalmomentum leads to that the momentum-dependent coupling constant stops runningin the critical region. As the result, the critical slowing down phenomenonreflecting the inherently IR effect doesn't take place at the critical pointfor the plasmon with finite external momentum.Comment: 4 pages, 2 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Critical behavior of the damping rate for a plasmon with finite momentum in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>theory

Critical behavior of the damping rate for a plasmon with finite momentum inφ4theory