Quantum critical scaling and the GrossNeveu model in 2+1 dimensions
Abstract
The quantum critical behavior of the (2+1)dimensional GrossNeveu model in the vicinity of its zerotemperature critical point is considered. The model is known to be renormalisable in the largeN limit, which offers the possibility to obtain expressions for various thermodynamic functions in closed form. We have used the concept of finitesize scaling to extract information about the leading temperature behavior of the free energy and the mass term, defined by the fermionic condensate and determined the crossover lines in the coupling (g)temperature (T) plane. These are given by T ~ g  g_{c}, where g_{c} denotes the critical coupling at zero temperature. According to our analysis no spontaneous symmetry breaking survives at finite temperature. We have found that the leading temperature behavior of the fermionic condensate is proportional to the temperature with the critical amplitude \frac{\sqrt{5}}3\pi . The scaling function of the singular part of the free energy is found to exhibit a maximum at \frac{\ln2}{2\pi} corresponding to one of the crossover lines. The critical amplitude of the singular part of the free energy is given by the universal number \frac{1}{3}\kern2pt\left[\frac1{2\pi}\zeta(3){Cl}_2\kern2pt\left(\frac{\pi}3\right)\right]=0.274543\ldots , where ζ(z) and Cl_{2}(z) are the Riemann zeta and Clausen's functions, respectively. Interpreted in terms of the thermodynamic Casimir effect, this result implies an attractive Casimir "force". This study is expected to be useful in shedding light on a broader class of four fermionic models.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 August 2011
 DOI:
 10.1209/02955075/95/40005
 arXiv:
 arXiv:1112.4853
 Bibcode:
 2011EL.....9540005C
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 6 pages, 3 figures