THEORY OF FINITE-TEMPERATURE CROSSOVERS NEAR QUANTUM CRITICAL-POINTS CLOSE TO, OR ABOVE, THEIR UPPER-CRITICAL DIMENSION

A systematic method for the computation of finite-temperature (T) cros sover functions near quantum-critical points close to, or above, their upper-critical dimension is devised. We describe the physics of the v arious regions in the T and critical tuning parameter (t) plane. The q uantum-critical point is at T = 0, t = 0, and in many cases there is a line of finite-temperature transitions at T = T-c(t), t < 0, with T-c (0) = 0. For the relativistic, n-component phi(4) continuum quantum fi eld theory [which describes lattice quantum rotor (n greater than or e qual to 2) and transverse field Ising (n = 1) models] the upper-critic al dimension is d = 3, and for d < 3, epsilon = 3-d is the control par ameter over the entire phase diagram. In the region \T - T-c(t)\ much less than T-c(t), we obtain an epsilon expansion for coupling constant s which then are input as arguments of known classical, tricritical, c rossover functions. In the high-T region of the continuum theory, an e xpansion in integer powers of root epsilon, module powers of ln epsilo n, holds for all thermodynamic observables, static correlators, and dy namic properties at all Matsubara frequencies; for the imaginary part of correlators at real frequencies (omega), the perturbative root epsi lon expansion describes quantum relaxation at (h) over bar omega simil ar to k(B)T or larger, but fails for (h) over bar omega similar to roo t epsilon k(B)T or smaller. An important principle, underlying the who le calculation, is the analyticity of all observables as functions of t at t = 0, for T > 0; indeed, analytic continuation in t is used to o btain results in a portion of the phase diagram. Our method also appli es to a large class of other quantum-critical points and their associa ted continuum quantum field theories.