Critical scaling in the $N=1$ Thirring Model in $(2+1)d$
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| Format: | Preprint |
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2026
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| _version_ | 1866909998064336896 |
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| author | Hands, Simon Worthy, Jude |
| author_facet | Hands, Simon Worthy, Jude |
| contents | 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 $\langle\barψψ\rangle$ 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 $N=2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_16051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical scaling in the $N=1$ Thirring Model in $(2+1)d$ Hands, Simon Worthy, Jude High Energy Physics - Lattice 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 $\langle\barψψ\rangle$ 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 $N=2$. |
| title | Critical scaling in the $N=1$ Thirring Model in $(2+1)d$ |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2601.16051 |