QUENCHED THERMODYNAMICS OF THE RANDOM BOND ISING-MODEL ON THE SQUARE LATTICE

The Ising model with randomly fluctuating bonds in two dimensions is considered. An effective field theory for the quenched thermodynamics of this model is derived and its properties are investigated in saddle point approximation. With g as the strength of the random fluctuations, the critical temperature Tc of the pure system is split into two critical temperatures T± = Tc(1 ± c0e-c1/g) with a Griffiths space for T- < T < T+. The Griffiths phase is characterized by spontaneous symmetry breaking which is related to a non-analyticity at g = 0. Therefore, one cannot apply an expansion in powers of g. However, this expansion is possible for T < T- and T > T+. Then the quenched specific heat, for instance, grows logarithmically (or double logarithmically close to T±) with |1 - T/Tc| up to a bound of the order 1/g. The quenched thermodynamic functions are also finite in the Griffiths phase with Griffiths singularities at T = T±. © 1990.