Long-Range Three-Particle Correlations at the Critical Point

A. K. Chaudhuri

Eiichi Hanamura, Shaul Mukamel

A microscopic correlation-function expression for the photon-echo signal in systems with long-range spatial correlations is developed. In general, the signal is given by an eight-point correlation function of the dipole operator involving two particles. In the absence of long-range spatial correlations, this correlation function may be factorized into a product of two four-point, single-particle correlation functions. Only under these conditions is the signal proportional to the absolute square of the ensemble-averaged nonlinear polarization. We predict that photon echoes may be used to probe the long-range spatial correlations near critical points.

A. K. Chaudhuri

Alan J. Bray

Random-field models are considered with long-range exchange, J(r) approximately 1/r d+ sigma , and/or long-range correlated random fields, (h(r)h(r')) approximately 1/ mod r-r' mod d- rho . A general scaling analysis is presented, in which the existence of three independent critical exponents is emphasized. Four different universality classes are identified, according to whether the fixed point controlling the critical behaviour is of short-range or long-range character for the exchange and/or the random-field correlations. The lines in the rho - sigma plane at which the long-range couplings first become relevant are expressed in terms of the exponents eta and eta of the corresponding short-range problem: long-range exchange is relevant for sigma <2- eta , long-range field correlations for rho >2 eta - eta . The scaling results are confirmed and amplified by explicit calculations of three independent exponents of the n-component spin model, correct to order 1/n. The results reveal errors in published expansions around the upper critical dimension.

Mikhail A. Anisimov, A. M. Evtyushenkov, Yu. F. Kiyachenko +1 more

Xiang-Mu Kong, Yang Zhan-Ru

In this paper dynamical critical phenomena of the Gaussian model with long-range interactions decaying as on d-dimensional hypercubic lattices (d = 1, 2, and 3) are studied. First, the critical points are exactly calculated, and it is found that the critical points depend on the value of δ and the range of interactions. Then the critical dynamics is considered. We calculate the time evolutions of the local magnetizations and the spin-spin correlation functions, and further the dynamic critical exponents are obtained. For one-, two- and three-dimensional lattices, it is found that the dynamic critical exponents are all which agrees with the result when only considering nearest neighboring interactions, and that they are all δ if It shows that the dynamic critical exponents are independent of the spatial dimensionality but depend on the value of δ.