Large-N transition temperature for superconducting films in a magnetic field

We consider the $N$-component Ginzburg-Landau model in the large $N$ limit, the system being embedded in an external constant magnetic field and confined between two parallel planes a distance $L$ apart from one another. On physical grounds, this corresponds to a material in the form of a film in the presence of an external magnetic field. Using techniques from dimensional and $zeta$-function regularization, modified by the external field and the confinement conditions, we investigate the behavior of the system as a function of the film thickness $L$. This behavior suggests the existence of a minimal critical thickness below which superconductivity is suppressed.Comment: Revtex, two column, 4 pages, 2 figure

Spontaneous Symmetry Breaking in Compactified λϕ4\lambda\phi^4 Theory

We consider the massive vector $N$-component $(\lambda\phi^{4})_{D}$ theory in Euclidian space and, using an extended Matsubara formalism we perform a compactification on a $d$-dimensional subspace, $d\leq D$. This allows us to treat jointly the effect of temperature and spatial confinement in the effective potential of the model, setting forth grounds for an analysis of phase transitions driven by temperature and spatial boundary. For $d=2$, which corresponds to the heated system confined between two parallel planes (separation $L$), we obtain, in the large $N$ limit at one-loop order, formulas for temperature- and boundary-dependent mass and coupling constant. The equation for the critical curve in the $\beta \times L$ plane is also derived.Comment: LATEX, 11 pages no figure

Non-Commutative Complete Mellin Representation for Feynman Amplitudes

We extend the complete Mellin (CM) representation of Feynman amplitudes to the non-commutative quantum field theories. This representation is a versatile tool. It provides a quick proof of meromorphy of Feynman amplitudes in parameters such as the dimension of space-time. In particular it paves the road for the dimensional renormalization of these theories. This complete Mellin representation also allows the study of asymptotic behavior under rescaling of arbitrary subsets of external invariants of any Feynman amplitude.Comment: 14 pages, no figur

Halperin-Lubensky-Ma effect in type-I superconducting films

In this note we employ concurrently techniques of generalized $zeta$-functions and compactification methods introduced in previous publications, to study the Halperin-Lubensky-Ma theory of induced weak first-order phase transitions applied to type-I superconducting films. We obtain closed formulas to the critical temperature and to the size temperature as functions of the film thickness.Comment: 4 pages, RevTex

Vacuum polarization in d+1/2d+{1/2} dimensions

We study the main properties of the one-loop vacuum polarization function ($\Pi_{\alpha \beta}$) for spinor $QED$ in `$d + {1/2}$ dimensions', i.e., with fields defined on ${\mathcal M} \subset {\mathbb R}^{d+1}$ such that ${\mathcal M} = \{(x_0,...,x_d) | x_{d}\geq 0 \}$, with bag-like boundary conditions on the boundary $\partial{\mathcal M} = \{(x_0,...,x_d) | x_{d}= 0 \}$. We obtain an exact expression for the induced current due to an external constant electric field normal to the boundary. We show that, for the particular case of 2+1 dimensions, there is a transverse component for the induced current, which is localized on a region close to $\partial{\mathcal M}$. This current is a parity breaking effect purely due to the boundary.Comment: 11 pages, no figure

One-loop dimensional reduction of the linear sigma model

We perform the dimensional reduction of the linear $\sigma$ model at one-loop level. The effective potential of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group equation which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum unstability of the model for large N.Comment: 19 pages, Latex, no figures, to be submitted to Physica

Finite-size effects on the chiral phase diagram of four-fermion models in four dimensions

We study the size dependence of the dynamical symmetry breaking in the four-dimensional Nambu-Jona-Lasinio model. We show that the presence of boundaries reduces the chiral breaking region, and this effect is strengthened for a larger number of compactified dimensions. A critical value for the length of the compactified dimensions exists, below which the dynamical symmetry breaking is not possible. Considering finite temperature and chemical potential, the chiral phase structure for the system with compactified dimensions is obtained. A gradual decreasing of the chiral breaking region with increasing of chemical potential is found. Also, at fixed chemical potential, the decreasing of the size of the system changes the order of the chiral phase transition.Comment: LATEX 14 pages 2 figure

The thermal coupling constant and the gap equation in the λϕD4\lambda\phi^{4}_{D} 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 $\lambda\phi^{4}$ 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

Dressed States Approach to Quantum Systems

Using the non-perturbative method of {\it dressed} states previously introduced in JPhysA, we study effects of the environment on a quantum mechanical system, in the case the environment is modeled by an ensemble of non interacting harmonic oscillators. This method allows to separate the whole system into the {\it dressed} mechanical system and the {\it dressed} environment, in terms of which an exact, non-perturbative approach is possible. When applied to the Brownian motion, we give explicit non-perturbative formulas for the classical path of the particle in the weak and strong coupling regimes. When applied to study atomic behaviours in cavities, the method accounts very precisely for experimentally observed inhibition of atomic decay in small cavities PhysLA, physics0111042