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We consider QED on a two-dimensional Euclidean torus with $f$ flavors ofmassless fermions and flavor-dependent chemical potentials. The dependence ofthe partition function on the chemical potentials is reduced to a$(2f-2)$-dimensional theta function. At zero temperature, the system can existin an infinite number of phases characterized by certain values of tracelessnumber densities and separated by first-order phase transitions. Furthermore,there exist many points in the $(f-1)$-dimensional space of traceless chemicalpotentials where two or three phases can coexist for $f=3$ and two, three, fouror six phases can coexist for $f=4$. We conjecture that the maximal number ofcoexisting phases grows exponentially with increasing $f$.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Phase structure of two-dimensional QED at zero temperature with  flavor-dependent chemical potentials and the role of multidimensional theta  functions