arXiv subjects

Jude Worthy

Publications and source records attributed to Jude Worthy.

7 recordsLinked to original sources

arXiv2026

Critical scaling in the $N=1$ Thirring Model in $(2+1)d$

The Thirring model in 2+1$d$ with $N$ Dirac flavors can exhibit spontaneous U($2N)\to$U($N)\otimes$U($N$) breaking through fermion - antifermion condensation in the limit $m\to0$. With no small parameter in play the symmetry-breaking dynamics is strongly-interacting and quantitative work requires a fermion formulation accurately capturing global symmetries. We present simulation results for $N=1$ obtained with Wilson kernel domain wall fermions on $16^3\times L_s$, with $L_s=24,\ldots,120$. The $L_s\to\infty$ extrapolation of the bilinear condensate $\langle\bar\psi\psi\rangle$ as a function of coupling and bare mass is fitted to an empirical equation of state; the resulting critical exponents are significantly altered from previously obtained values, and for the first time resemble those emerging from analytic predictions based on approximate solutions to Schwinger-Dyson equations, consistent with a putative UV-stable renormalisation group fixed point. To address the non-perturbative issue of the value $N_c$ below which such a fixed point exists we present preliminary results obtained with $N=2$.

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arXiv2025

Critical Behaviour in the Single Flavor Thirring Model in 2+1$d$ with Wilson Kernel Domain Wall Fermions

We present results of a lattice field theory simulation of the 2+1$d$ Thirring model with $N=1$ fermion flavors, using domain wall fermions. The model exhibits a U(2) symmetry-breaking phase transition with the potential to define a UV-stable renormalisation group fixed point. The novelty is the replacement of the Shamir kernel used in all previous work with the Wilson kernel, improving the action particularly with respect to the $L_s\to\infty$ limit needed to recover U(2), now under much better control. Auxiliary field ensembles generated on $16^3\times24$ with varying self-interaction strength $g^2$ and bare mass $m$ are used to measure the bilinear condensate order parameter $\langle\bar\psi i\gamma_3\psi\rangle$ with domain wall separations as large as $L_s=120$. The resulting $L_s\to\infty$ extrapolation is used to fit an empirical equation of state modelling spontaneous symmetry breaking as $m\to0$. The fit is remarkably stable and compelling, with the fitted critical exponents $\beta_m\simeq2.4$, $\delta\simeq1.3$ differing markedly from previous estimates. The associated susceptibility exhibits a mass hierarchy in line with physical expectations, again unlike previous estimates. Schwinger-Dyson equation (SDE) solutions of the Thirring model exploiting a hidden local symmetry in the action are reviewed, and analytic predictions presented for the exponents. In contrast to all previous lattice studies, the universal characteristics of the critical point revealed qualitatively resemble the SDE predictions.

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arXiv2024

Evaluation of the Bilinear Condensate of the Planar Thirring Model in the Strongly Coupled Region

The planar Thirring model is thought to have a strongly coupled critical point for a single flavour of fermion. We look at the calculation of the bilinear condensate in this critical region, and its characterisation via an equation of state. Since the computation is numerically challenging we investigate improved Dirac operators. We present findings on different methods of calculation using a rational hybrid Monte Carlo scheme, and calculations of the bilinear condensate, an equation of state, and the associated critical exponents. Overlap and domain wall Dirac operators, and variants therein are considered.

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arXiv2023

The Thirring Model in 2+1$d$ with Optimised Domain Wall Fermions

After briefly reviewing the potential for the $N$-flavor Thirring model, formulated with reducible fermions in 2+1$d$, to exhibit a strongly-coupled UV-stable fixed point where U($2N$) symmetry is spontaneously broken by a fermion bilinear condensate, we present recent lattice studies using the Domain Wall Fermion formulation. In particular, we focus on possible improved methods for extracting the necessary $L_s\to\infty$ limit, where $L_s$ is the wall separation, through a combination of partial quenching (ie. $L_s({\rm valence})>L_s({\rm sea})$), replacing the Shamir kernel with the Wilson kernel in the definition of the overlap operator, and improved estimation of the signum function using the Zolotarev approximation. Equation of state fits for critical exponents on $12^3$ systems yield encouraging agreement between distinct approaches, consistent with universal scaling, while contradicting earlier fits based on a naive extrapolation. The new results are also in tension with old results obtained with staggered fermions.

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arXiv2021

Properties of Overlap and Domain Wall Fermions in the 2+1D Thirring Model

We present some results pertaining to partially quenched formulations of the overlap/domain wall operator with the Thirring model in 2+1D. Auxiliary fields are generated with a Shamir domain wall approach and measurements of eigenvalues and condensates are contrasted with different overlap operators. The numerical challenge posed by a non-compact formulation is highlighted, and the effective use of lower accuracy sea fermions is demonstrated.

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arXiv2021

Critical Behaviour in the Single Flavor Planar Thirring Model

We report results of simulations of the $2+1d$ Thirring model with $N$ fermion flavors, defined on a lattice using domain wall fermions. This approach is devised to respect as far as possible the underlying U($2N$) symmetry of the continuum model, expected to be recovered in the limit wall separation $L_s\to\infty$. For $N=1$ there is a symmetry-breaking phase transition associated with bilinear condensation at strong fermion self-interaction, which is a plausible location for a quantum critical point. Fits to a renormalisation group-inspired equation of state yield critical exponents distinct from those obtained using a version of the model defined using staggered fermions.

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arXiv2020

Critical Behaviour in the Single Flavor Thirring Model in 2+1d

Results of a lattice field theory simulation of the single-flavor Thirring model in 2+1 spacetime dimensions are presented. The lattice model is formulated using domain wall fermions as a means to recover the correct U(2) symmetries of the continuum model in the limit where wall separation $L_s\to\infty$. Simulations on $12^3, 16^3\times L_s$, varying self-interaction strength $g^2$ and bare mass $m$ are performed with $L_s = 8, \ldots 48$, and the results for the bilinear condensate $\langle\barψψ\rangle$ fitted to a model equation of state assuming a U(2)$\to$U(1)$\otimes$U(1) symmetry-breaking phase transition at a critical $g_c^2$. First estimates for $g^{-2}a$ and critical exponents are presented, showing small but significant departures from mean-field values. The results confirm that a symmetry-breaking transition does exist and therefore the critical number of flavors for the Thirring model $N_c > 1$. Results for both condensate and associated susceptibility are also obtained in the broken phase on $16^3\times48$, suggesting that here the $L_s\to\infty$ extrapolation is not yet under control. We also present results obtained with the associated 2+1$d$ truncated overlap operator DOL demonstrating exponential localisation, a necessary condition for the recovery of U(2) global symmetry, but that recovery of the Ginsparg-Wilson condition as $L_s\to\infty$ is extremely slow in the broken phase.

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