Critical Behaviour in the Dense Planar NJL Model

Simon Hands; Biagio Lucini; Susan Morrison

doi:10.1103/physrevlett.86.753

Home/Archive/arXiv

arXiv · hep-lat/0008027

Critical Behaviour in the Dense Planar NJL Model

Simon Hands·Biagio Lucini·Susan Morrison

View original source ↗Read source document ↗Export metadata ↓

Abstract

We present results of a Monte Carlo simulation of a 2+1 dimensional Nambu - Jona-Lasinio model including diquark source terms. A diquark condensate is measured as a function of source strength j. In the vacuum phase vanishes linearly with j as expected, but simulations in a region with non-zero baryon density suggest a power-law scaling and hence a critical system for all mu > mu_c. There is no diquark condensation signalling superfluidity. Comparisons are drawn with known results in two dimensional theories, and with the pseudogap phase in cuprate superconductors. We also measure the dispersion relation E(k) for fermionic excitations, and find results consistent with a sharp Fermi surface. Any superfluid gap Delta is constrained to be much less than the constituent quark mass scale Sigma_0.

Explore related subjects

hep-lat cond-mat.supr-con hep-ph nucl-th

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Simon Hands, Biagio Lucini, Susan Morrison. 2000-08-31. Critical Behaviour in the Dense Planar NJL Model. https://doi.org/10.1103/physrevlett.86.753

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Symplectic lattice gauge theories in the Grid framework: domain wall fermions and continuum extrapolations

We report the results of the first numerical lattice study using domain-wall fermions in the Sp(4) gauge theory coupled to two flavours of (Dirac) fermions, transforming in the fundamental representation of the gauge group. This theory plays a prominent role in the literature on extensions of the Standard Model with composite dynamics. It provides a short-distance completion for a class of composite Higgs models, or, alternatively, of dark matter models based on the strongly interacting massive particle paradigm. We adopt the Möbius formulation of domain-wall fermions (MDWF), implemented within the Grid software environment. We report the results of extensive tests of the algorithm implementation, and of the optimisation of the choices of algorithmic parameters appearing in the MDWF action. We then measure masses and decay constants of the lightest flavoured mesons in ensembles with moderately large fermion masses and several choices of lattice coupling, and perform an extrapolation to the continuum. We compare our results for the physical observables to published measurements obtained in the same field theory, but derived on the lattice by employing Wilson fermions. We demonstrate that, with the deployment of moderate computational resources, the MDWF formulation can yield order-of-magnitude gains in the approach to the continuum limit, in regions of physical parameter space relevant to phenomenological applications of this theory.

hep-lat↗

arXiv2026

Numerical Investigations of Phase Transitions in Lattice Field Theories

The study of phase transitions plays an important role in understanding qualitative changes in the behaviour of physical systems at criticality. Despite decades of progress, there is still a strong demand for high-precision numerical tools capable of resolving subtle critical phenomena. Motivated by this need, in this thesis, we present two complementary numerical investigations of phase transitions in lattice systems. The first uses GPU-accelerated higher-order tensor renormalization group (HOTRG) techniques to study the two-dimensional generalized XY model, characterizing its ferromagnetic, nematic, and paramagnetic phases and mapping their phase boundaries using thermodynamic observables in the thermodynamic limit. The second develops and benchmarks a configurational temperature estimator, constructed from gradients and Hessians of the Euclidean lattice action, in compact U(1) lattice gauge theories. On one hand, tensor network methods capture rich phase structures when truncation and finite-bond effects are adequately controlled. On the other hand, the configurational temperature estimator provides an independent, low-overhead means of validating thermal sampling across different algorithms and models, and can also be used as a runtime diagnostic to identify sampling pathologies before large-scale production runs.

hep-lat↗

arXiv2026

Computability of GPDs near $x=\pmξ$ in Lattice QCD

In lattice QCD computations of generalized parton distributions (GPDs), the large momentum expansion generally requires all hard scales, $2|x\pmξ|P^z$ and $2|1\pm x|P^z$, to be much larger than $Λ_{\rm QCD}$. We show that this condition can be relaxed for $2|x\pmξ|P^z$ at large $ξ$, making the important $x\sim\pmξ$ regions accessible to lattice calculations and considerably expanding the region of computability. Revisiting previous lattice results with complete one-loop matching, we obtain the expected partonic threshold behavior---GPDs continuous at $x=\pmξ$ but with discontinuous derivatives---which has not previously been observed on the lattice. We thus obtain, for the first time, important prediction for GPDs in the distribution-amplitude-like region, which smoothly connects the quark and antiquark PDF-like behaviors.

hep-lat↗