The Dyson–Schwinger equations of Landau-gauge Yang–Mills theory for the gluon and ghost propagators are investigated. Numerical results are obtained within a truncation scheme which has proven to be successful at vanishing temperature. For temperatures up to 250 MeV we find only minor quantitative changes in the infrared behaviour of the gluon and ghost propagators. The effective action calcula...

We study the finite temperature crossovers in the vicinity of a zero temperature quantum phase transition. The universal crossover functions are observables of a continuum quantum field theory. Particular attention is focussed on the high temperature limit of the continuum field theory, the socalled “quantum-critical” region. Basic features of crossovers are illustrated by a simple solvable mod...

We analyze the phemomenon of induced fermion number at finite temperature. At finite temperature, the induced fermion number 〈N〉 is a thermal expectation value, and we compute the finite temperature fluctuations, (∆N) = 〈N〉 − 〈N〉. While the zero temperature induced fermion number is topological and is a sharp observable, the finite temperature induced fermion number is generically nontopologica...

We study the finite temperature crossovers in the vicinity of a zero temperature quantum phase transition. The universal crossover functions are observables of a continuum quantum field theory. Particular attention is focussed on the high temperature limit of the continuum field theory, the socalled “quantum-critical” region. Basic features of crossovers are illustrated by a simple solvable mod...

We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field and their free energy cost is determined by the finite-temperature fixed point exponents. In this framework, numerical results suggest that mean...

We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the random field Ising model. Within the replica formalism, we treat the quenched random field as an annealed spin variable, thereby avoiding the usual average over the random field distribution. This allows to study the influence of the distribution on t...

Recent developments of perturbation theory at finite temperature based on effective field theory methods are reviewed. These methods allow the contributions from the different scales to be separated and the perturbative series to be reorganized. The construction of the effective field theory is shown in detail for φ4 theory and QCD. It is applied to the evaluation of the free energy of QCD at o...