Effects of long-range interaction on critical and multicritical behavior of compressible disordered systems

A field-theoretic approach is applied to describe behavior of weakly disordered, isotropic elastic compressible systems with long-range interactions directly in the three-dimensional space for various values of the long-range interaction parameter a. A renormalization-group procedure is applied separately for a > 2 and a ≤ 2 directly in the three-dimensional space. Renormalization-group equations are analyzed in the two-loop approximation, and critical and tricritical points are determined. It is shown that long-range effects are not important when a ≤ 2, whereas they play a key role in the opposite case of a > 2. Critical exponents characterizing the system are obtained for various values of the long-range interaction parameter. Behavior of homogeneous and disordered systems characterized by two fluctuating order parameters is also described.