4 research outputs found
Dimensional reduction of the chiral-continous Gross-Neveu model
We study the finite-temperature phase transition of the generalized
Gross-Neveu model with continous chiral symmetry in euclidean
dimensions. The critical exponents are computed to the leading order in the
expansion at both zero and finite temperatures. A dimensionally reduced
theory is obtained after the introduction of thermal counterterms necessary to
cancel thermal divergences that arise in the limit of high temperature.
Although at zero temperature we have an infinitely and continously degenerate
vacuum state, we show that at finite temperature this degeneracy is discrete
and, depending on the values of the bare parameters, we may have either total
or partial restoration of symmetry. Finally we determine the universality class
of the reduced theory by a simple analysis of the infrared structure of
thermodynamic quantities computed using the reduced action as starting point.Comment: Latex, 25 pages, 4 eps fig., uses epsf.sty and epsf.te
The thermal coupling constant and the gap equation in the model
By the concurrent use of two different resummation methods, the composite
operator formalism and the Dyson-Schwinger equation, we re-examinate the
behavior at finite temperature of the O(N)-symmetric model in
a generic D-dimensional Euclidean space. In the cases D=3 and D=4, an analysis
of the thermal behavior of the renormalized squared mass and coupling constant
are done for all temperatures. It results that the thermal renormalized squared
mass is positive and increases monotonically with the temperature. The behavior
of the thermal coupling constant is quite different in odd or even dimensional
space. In D=3, the thermal coupling constant decreases up to a minimum value
diferent from zero and then grows up monotonically as the temperature
increases. In the case D=4, it is found that the thermal renormalized coupling
constant tends in the high temperature limit to a constant asymptotic value.
Also for general D-dimensional Euclidean space, we are able to obtain a formula
for the critical temperature of the second order phase transition. This formula
agrees with previous known values at D=3 and D=4.Comment: 23 pages, 4 figure
SO(2,1) conformal anomaly: Beyond contact interactions
The existence of anomalous symmetry-breaking solutions of the SO(2,1)
commutator algebra is explicitly extended beyond the case of scale-invariant
contact interactions. In particular, the failure of the conservation laws of
the dilation and special conformal charges is displayed for the two-dimensional
inverse square potential. As a consequence, this anomaly appears to be a
generic feature of conformal quantum mechanics and not merely an artifact of
contact interactions. Moreover, a renormalization procedure traces the
emergence of this conformal anomaly to the ultraviolet sector of the theory,
within which lies the apparent singularity.Comment: 11 pages. A few typos corrected in the final versio