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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.14490 |
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| _version_ | 1866915006767955968 |
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| author | David, Justin R. Kumar, Srijan |
| author_facet | David, Justin R. Kumar, Srijan |
| contents | We evaluate the thermal one point function of higher spin currents in the critical model of $U(N)$ complex scalars interacting with a quartic potential and the $U(N)$ Gross-Neveu model of Dirac fermions at large $N$ and strong coupling using the Euclidean inversion formula. These models are considered in odd space time dimensions $d$ and held at finite temperature and finite real chemical potential $μ$ measured in units of the temperature. We show that these one point functions simplify both at large spin and large $d$. At large spin, the one point functions behave as though the theory is free, the chemical potential appears through a simple pre-factor which is either $\coshμ$ or $\sinhμ$ depending on whether the spin is even or odd. At large $d$, but at finite spin and chemical potential, the 1-point functions are suppressed exponentially in $d$ compared to the free theory. We study a fixed point of the critical Gross-Neveu model in $d=3$ with 1-point functions exhibiting a branch cut in the chemical potential plane. The critical exponent for the free energy or the pressure at the branch point is $3/2$ which coincides with the mean field exponent of the Lee-Yang edge singularity for repulsive core interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14490 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | One point functions in large $N$ vector models at finite chemical potential David, Justin R. Kumar, Srijan High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons We evaluate the thermal one point function of higher spin currents in the critical model of $U(N)$ complex scalars interacting with a quartic potential and the $U(N)$ Gross-Neveu model of Dirac fermions at large $N$ and strong coupling using the Euclidean inversion formula. These models are considered in odd space time dimensions $d$ and held at finite temperature and finite real chemical potential $μ$ measured in units of the temperature. We show that these one point functions simplify both at large spin and large $d$. At large spin, the one point functions behave as though the theory is free, the chemical potential appears through a simple pre-factor which is either $\coshμ$ or $\sinhμ$ depending on whether the spin is even or odd. At large $d$, but at finite spin and chemical potential, the 1-point functions are suppressed exponentially in $d$ compared to the free theory. We study a fixed point of the critical Gross-Neveu model in $d=3$ with 1-point functions exhibiting a branch cut in the chemical potential plane. The critical exponent for the free energy or the pressure at the branch point is $3/2$ which coincides with the mean field exponent of the Lee-Yang edge singularity for repulsive core interactions. |
| title | One point functions in large $N$ vector models at finite chemical potential |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2406.14490 |