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Certain phase transitions in a graphene sheet are known to be described at criticality by an underlying continuum quantum field theory which is the Gross-Neveu model. While the Ising Gross-Neveu model has been widely studied for many years, perturbative and large N computations in the related chiral Heisenberg Gross-Neveu model have not been carried out to the same level of precision. In the talk we will review recent four loop renormalization of the Ising Gross-Neveu model before developing the large N expansion for the chiral Heisenberg Gross-Neveu case. In the latter case the first three terms of various critical exponents are determined including eta at O(1/N^3). To achieve this accuracy the large N conformal bootstrap method is used. Finally estimates of exponents are given for the values of N relevant to the graphene transitions and compared to Monte Carlo and functional renormalization group results as well as the epsilon expansion of four dimensional perturbation theory.

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John Gracey, University of Liverpool
Seminar room 0.03, ETP
Contact: Michael Scherer