Critical exponents without the epsilon expansion

Critical Exponents without the Epsilon Expansion

We argue that the sharp-cuto Wilson renormalization group provides a powerful tool for the analysis of second-order and weakly rst-order phase transitions. In particular, in a computation no harder than the calculation of the 1-loop e ective potential, we show that the Wilson RG yields the xed point couplings and critical exponents of 3-dimensional O(N) scalar eld theory, with results close to ...

Accurate critical exponents from the -expansion

Critical exponents and the pseudo-ǫ expansion

We present the pseudo-ǫ expansions (τ -series) for the critical exponents of a λφ4 threedimensional O(n)-symmetric model obtained on the basis of six-loop renormalization-group expansions. Concrete numerical results are presented for physically interesting cases n = 1, n = 2, n = 3 and n = 0, as well as for 4 ≤ n ≤ 32 in order to clarify the general properties of the obtained series. The pseudo...

Expansion Exponents for Nonequilibrium Systems

Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of calculating the exponents are discussed. The principle of minimal expansion provides the basis for treating the problem of pattern selection. The exponents are al...

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...