Abstract
We studied the three dimensional Thirring model in the limit of infinite number of flavors at finite temperature and density. We calculated the number density as a function of temperature and the density at zero temperature serves as a relevant parameter. A three dimensional free fermion gas behavior as the density at zero temperature approaches zero smoothly crosses over to a two dimensional free fermion gas behavior as the density at zero temperature approaches infinity.
Highlights
AND SUMMARYThe three-dimensional Euclidean (two spatial and one thermal) Thirring model with N flavors of two-component fermions would have been deemed nonrenormalizable by a standard power counting argument but it has been shown to be renormalizable in a
We have studied the three-dimensional Euclidean Thirring model at finite temperature and chemical model in the limit of infinite number of flavors and our aim was to understand the relevance of the Thirring coupling
The effective action is complex and we had to perform an extensive graphical analysis to show that one particular saddle point dominates over all other possible saddle points at all chemical potential and temperature
Summary
The three-dimensional Euclidean (two spatial and one thermal) Thirring model with N flavors of two-component fermions would have been deemed nonrenormalizable by a standard power counting argument but it has been shown to be renormalizable in a. We explore the relevance of the Thirring coupling in the large N limit at finite temperature and density. The relevance of the Thirring coupling is already seen by noticing that the number density at zero temperature smoothly crosses over from μ2 4π as μ→0 to pμffiffiffiaffiffisffiffiffiffiμffi → ∞. Defining a reduced temperature by T 1⁄4 4πn0t and writing the number density as a function of temperature as nðn0; tÞn0, we will show that nðn0; tÞ is the solution to nðn0; tÞ 1⁄4 8t2r2 þ qffiffiffiffi n0 4π. This result for the number density is plotted as a function of temperature in Fig. 1 and shows that it smoothly crosses over from a three-dimensional free fermion gas as n0 → 0 to a two-dimensional free fermion gas as n0 → ∞. We set up our notation for the three-dimensional Thirring model and arrive at the saddle point equations in the limit of N → ∞ in
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