Condensation of Lee-Yang zeros in scalar field theory

Abstract

We show that, at the critical temperature, there is a class of Lee-Yang zeros of the partition function in a general scalar field theory, which location scales with the size of the system with a characteristic exponent expressed in terms of the isothermal critical exponent δ. In the thermodynamic limit the zeros belonging to this class condense to the critical point ζ=1 on the real axis in the complex fugacity plane while the complementary set of zeros (with Reζ<1) covers the unit circle. Although the aforementioned class degenerates to a single point for an infinite system, when the size is finite it contributes significantly to the partition function and reflects the self-similar structure (fractal geometry, scaling laws) of the critical system. This property opens up the perspective to formulate finite-size scaling theory in effective QCD, near the chiral critical point, in terms of the location of Lee-Yang zeros.

QCD phase diagram from chiral symmetry restoration: analytic approach at high and low temperature using the Linear Sigma Model with Quarks

“…Future experiments [2][3][4] will keep on conducting a thorough exploration of the transition from confined/chiral-symmetry broken hadron matter to the deconfined/chiral-symmetry restored state, varying the temperature and baryon density by changing the collision energy down to about √ s N N 5 GeV and the system size in hadron and heavy-ion reactions. From the theoretical side, efforts to locate the CEP employing a variety of techniques such as Schwinger-Dyson equations, finite energy sum rules, functional renormalization methods, holography, and effective models, have produced a wealth of results [5][6][7][8][9][10][11][12][13][14][15][16] ranging from low to large values of the baryon chemical potential (µ B ) and temperature (T ). Recent lattice QCD (LQCD) analyses [17] have resorted to using the imaginary baryon chemical potential technique, to later extrapolate to real values, to study the chiral transition near the T -axis.…”