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Low‐temperature renormalization group study of the random spin systems
Author(s) -
Li Mai Xuan,
Duc Nguyen Manh
Publication year - 1981
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221070203
Subject(s) - fixed point , renormalization group , condensed matter physics , critical exponent , phase transition , physics , critical point (mathematics) , impurity , order (exchange) , spin (aerodynamics) , critical dimension , critical phenomena , statistical physics , mathematical physics , mathematics , thermodynamics , quantum mechanics , mathematical analysis , finance , economics
The second‐order phase transition of a weakly disordered system in 2 + ϵ dimensions is investigated by means of the low‐temperature renormalization group technique. It is shown that there are two fixed points: the Migdal‐Polyakov and the unphysical ones. As the Migdal‐Polyakov fixed point is always stable it is concluded that the disordered and the ordered systems have the same critical exponents. These results agree with the Harris hypothesis, which predicts that phase transitions with positive value of α do not occur in the presence of quenched disorder. The effects of the long‐range exchange interaction on the critical behaviour of the quenched system in σ + ϵ dimensions are also discussed. The criteria for the concentration of nonmagnetic impurities in the systems under consideration are established.