Permissible overheating of the gaseous medium in a gas-flow laser excited by fission fragments from uranium nuclei

Abstract

We present the critical exponents ν L2 , η L2 and γ L for an m-axial Lifshitz point at second order in an L expansion. We introduce a constraint involving the loop momenta along the m-dimensional subspace in order to perform two-and three-loop integrals. The results are valid in the range 0 m < d. The case m = 0 corresponds to the usual Ising-like critical behaviour.PACS numbers: 7540, 0550, 1110, 6460K, 7540C Lifshitz multicritical points appear at the confluence of a disordered phase, a uniformly ordered phase and a modulated ordered phase [1,2]. The spatially modulated phase is characterized by a fixed equilibrium wavevector k 0 . In this phase, k 0 goes continuously to zero as the system approaches the Lifshitz point. If this wavevector has m components, the critical system under consideration presents an m-fold Lifshitz critical behaviour. This sort of critical behaviour is present in a variety of real physical systems including high-T c superconductors [3][4][5], ferroelectric liquid crystals [6,7], magnetic compounds and alloys [8-10], among others.In magnetic systems [11], the m-fold Lifshitz point can be described by a spin-1 2 Ising model on a d-dimensional lattice with nearest-neighbour ferromagnetic interactions as well as next-nearest-neighbour competing antiferromagnetic couplings along m directions. This system can be described in a field-theoretic setting using a modified φ 4 theory with higherorder derivative terms, which arises as an effect of the competition along the m directions. The Lifshitz universality class is defined by the parameters (N, d, m), where N is the number of components of the order parameter, d is the space dimension of the system and m is the number of competing directions.Other examples of field theories containing higher derivative terms have been investigated in different physical scenarios. In cosmology, the recently proposed model known as 'kinflation' describes inflation driven by higher-order kinetic terms for the inflaton scalar field [12]. Another instance which arises in quantum field theory in curved spacetime is the quantization of scalar fields with a high-frequency dispersion relation around a classical gravitational background [13,14]. In this case, the higher-order term accounts for deviations