Nonequilibrium critical phenomena in one-component reaction-diffusion systems

Nonequilibrium critical phenomena in one-component reaction-diffusion systems are investigated on the basis of a mean-field theory and/or a field-theoretic renormalization-group technique. A superposition of three reactions of type mX→m’X (m>m’), mX→m’ ’X (m’’), and nX→n’X (n>n’, n>m>0), which represents all universality classes of second-order phase transitions in one-component reaction-diffusion systems, is considered. The upper critical dimension is given by $d_c$=2(n-m+1)/(n-1). Mean-field values of critical exponents are determined as a function of the order of reactions, m, and n. In addition, critical exponents for the process m=1 and n=3 are calculated to first order in ɛ=$d_c$-d ($d_c$=3) by an ɛ-expansion method. Critical exponents depend on m and n and phase transitions in different order reaction systems belong to different universality classes. It should be emphasized that the autocatalytic nature of the process causes the breakdown of the fluctuation-dissipation theorem and associated two different (probably independent in higher-order systems) susceptibility exponents: the static susceptibility exponent describing spatial fluctuations at steady states and the dynamic susceptibility exponent characterizing time evolution of the process.