相关论文: A finite temperature generalization of Zamolodchik…
In this paper we examine the behavior in temperature of the free energy on quantum systems in an arbitrary number of dimensions. We define from the free energy a function $C$ of the coupling constants and the temperature, which in the…
A fundamental quantity in 1+1 dimensional quantum field theories is Zamolodchikov's c-function. A function of a renormalization group distance parameter r that interpolates between UV and IR fixed points, its value is usually interpreted as…
We discuss the possibility of generalizing some aspects of the C-theorem within two different approaches, the conventional RG and the Wilson RG flows. We show that the original Zamolodchikov's theorem is related to the existence of the…
The behavior of the finite-temperature C-function, defined by Neto and Fradkin [Nucl. Phys. B {\bf 400}, 525 (1993)], is analyzed within a d -dimensional exactly solvable lattice model, recently proposed by Vojta [Phys. Rev. B {\bf 53}, 710…
The relative entropy in two-dimensional Field Theory is studied for its application as an irreversible quantity under the Renormalization Group, relying on a general monotonicity theorem for that quantity previously established. In the…
We elaborate on a previous attempt to prove the irreversibility of the renormalization group flow above two dimensions. This involves the construction of a monotonically decreasing $c$-function using a spectral representation. The missing…
The relative entropy in two-dimensional field theory is studied on a cylinder geometry, interpreted as finite-temperature field theory. The width of the cylinder provides an infrared scale that allows us to define a dimensionless relative…
We discuss an extension of the $C$-theorem to chiral theories. We show that two monotonically decreasing $C$-functions can be introduced. However, their difference is a constant of the renormalization group flow. This constant reproduces…
We examine the thermal behavior of a theory with charged massive vector matter coupled to Chern-Simons gauge field. We obtain a critical temperature Tc, at which the effective mass of vector field vanishes, and the system transfers from a…
One of the fundamental questions in Quantum Field Theory regards the determination of a measure of the degrees of freedom of theories that is consistent with the Renormalization Group flow. The answer seems to be encoded in the C-theorems,…
A new approach to quantum field theory at finite temperature and density in arbitrary space-time dimension D is developed. We focus mainly on relativistic theories, but the approach applies to non-relativistic ones as well. In this…
The Zamolodchikov c-theorem has led to important new insights in our understanding of the renormalisation group and the geometry of the space of QFTs. Here, we review the parallel developments of the search for a higher-dimensional…
In the limit where $N\to\infty$ and the coupling constant $g \to g_{c}$ in a correlated manner, O(N) symmetric vector models represent filamentary surfaces. The purpose of these studies is to gain intuition for the long lasting search for a…
We formalize and prove the extension to finite temperature of a class of quantum phase transitions, acting as condensations in the space of states, recently introduced and discussed at zero temperature~(Ostilli and Presilla 2021 \textit{J.…
In these notes we review some properties of Statistical Quantum Field Theory at equilibrium, i.e Quantum Field Theory at finite temperature. We explain the relation between finite temperature quantum field theory in (d,1) dimensions and…
A proof for a non-perturbative C-theorem in four dimensions, capturing the irreversibility of the renormalization group flow in the space of unitary quantum field theories, has not been accomplished, yet. We test the conjectured C-theorems…
The trace of the heat kernel in a (D+1)-dimensional Euclidean spacetime (integer D > 1) is used to derive the free energy in finite temperature field theory. The spacetime presents a D-dimensional compact space (domain) with a…
We present a proof of the irreversibility of renormalization group flows, i.e. the c-theorem for unitary, renormalizable theories in four (or generally even) dimensions. Using Ward identities for scale transformations and spectral…
The combination of the Lorentz symmetry and the strong subadditive property of the entropy leads to a c-theorem for the entanglement entropy in 1+1 dimensions. We present a simple derivation of this theorem and compare the associated…
We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction…