Search results for "Sigma model"
showing 10 items of 19 documents
Friedel Oscillations in Relativistic Nuclear Matter
1994
We calculate the low-momentum N-N effective potential obtained in the OBE approximation, inside a nuclear plasma at finite temperature, as described by the relativistic $ \sigma $-$ \omega $ model. We analyze the screening effects on the attractive part of the potential in the intermediate range as density or temperature increase. In the long range the potential shows Friedel-like oscillations instead of the usual exponential damping. These oscillations arise from the sharp edge of the Fermi surface and should be encountered in any realistic model of nuclear matter.
Fixed points of nonlinear sigma models in d>2
2009
Using Wilsonian methods, we study the renormalization group flow of the Nonlinear Sigma Model in any dimension $d$, restricting our attention to terms with two derivatives. At one loop we always find a Ricci flow. When symmetries completely fix the internal metric, we compute the beta function of the single remaining coupling, without any further approximation. For $d>2$ and positive curvature, there is a nontrivial fixed point, which could be used to define an ultraviolet limit, in spite of the perturbative nonrenormalizability of the theory. Potential applications are briefly mentioned.
Free field realization of cylindrically symmetric Einstein gravity
1998
Cylindrically reduced Einstein gravity can be regarded as an $SL(2,R)/SO(2)$ sigma model coupled to 2D dilaton gravity. By using the corresponding 2D diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst equation we show that the theory can be mapped by a canonical transformation into a set of free fields with a Minkowskian target space. We briefly discuss the quantization in terms of these free-field variables, which is considerably simpler than in the other approaches.
Conformal and non-conformal symmetries in 2D dilaton gravity
1996
We introduce new extra symmetry transformations for generic 2D dilaton-gravity models. These symmetries are non-conformal but special linear combinations of them turn out to be the extra (conformal) symmetries of the CGHS model and the model with an exponential potential. We show that one of the non-conformal extra symmetries can be converted into a conformal one by means of adequate field redefinitions involving the metric and the derivatives of the dilaton. Finally, by expressing the Polyakov-Liouville effective action in terms of an auxiliary invariant metric, we construct one-loop models which maintain the extra symmetry of the classical action. © 1997 Elsevier Science B.V.
Effective models of two-flavor QCD: from small towards large $m_q$
2009
We study effective models of chiral fields and Polyakov loop expected to describe the dynamics responsible for the phase structure of two-flavor QCD. We consider the chiral sector described either using a linear sigma model or a Nambu-Jona-Lasinio model and study how these models, on the mean-field level when coupled with the Polyakov loop, behave as a function of increasing bare quark (or pion) mass. We find qualitatively similar behaviors for the cases of the linear sigma model and the Nambu-Jona-Lasinio model and, by comparing with existing lattice data, show that one cannot conclusively decide which of the two approximate symmetries drives the phase transitions at the physical point.
The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
2021
The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the $O(3)$ non-linear sigma model in $1+1$ dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in $3+1$ dimensio…
Finite size spectrum of SU(N) principal chiral field from discrete Hirota dynamics
2016
Using recently proposed method of discrete Hirota dynamics for integrable (1+1)D quantum field theories on a finite space circle of length L, we derive and test numerically a finite system of nonlinear integral equations for the exact spectrum of energies of SU(N)xSU(N) principal chiral field model as functions of m L, where m is the mass scale. We propose a determinant solution of the underlying Y-system, or Hirota equation, in terms of determinants (Wronskians) of NxN matrices parameterized by N-1 functions of the spectral parameter, with the known analytical properties at finite L. Although the method works in principle for any state, the explicit equations are written for states in the …
What is the Right Theory for Anderson Localization of Light? An Experimental Test
2018
Anderson localization of light is traditionally described in analogy to electrons in a random potential. Within this description, the random potential depends on the wavelength of the incident light. For transverse Anderson localization, this leads to the prediction that the distribution of localization lengths---and, hence, its average---strongly depends on the wavelength. In an alternative description, in terms of a spatially fluctuating electric modulus, this is not the case. Here, we report on an experimentum crucis in order to investigate the validity of the two conflicting theories using optical samples exhibiting transverse Anderson localization. We do not find any dependence of the …
Degrees of freedom and the phase transitions of two-flavor QCD
2008
We study two effective models for QCD, the Nambu-Jona-Lasinio -model and the linear sigma model extended by including a Polyakov loop potential, which is fitted to reproduce the pure gauge theory thermodynamics, and a coupling between the chiral fields and the Polyakov loop. Thus the resulting models have as relevant degrees of freedom the Polyakov loop and chiral fields. By comparing the extended models with the bare chiral models we can conclude that the addition of the Polyakov loop is necessary in order to obtain both qualitative and quantitative agreement with known results at finite temperatures. These results are extended to finite net-quark densities, several thermodynamical quantit…
Classical and Quantum Nonultralocal Systems on the Lattice
1997
We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix. A nonultralocal quantum algebras on the lattices for these systems are constructed. For some class of such algebras an ultralocalization procedure is proposed. The technique of the modified Bethe-Anzatz for these algebras is developed and is applied to the nonlinear sigma model problem.