Related papers: Hidden superuniversality in systems with continuou…
Renormalization group theory does not restrict the from of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts,…
The Ashkin-Teller (AT) model is a generalization of Ising 2-d to a four states spin model; it can be written in the form of two Ising layers (in general with different couplings) interacting via a four-spin interaction. It was conjectured…
The $N$-color Ashkin-Teller model corresponds to $N$ Ising models coupled by four-spin interactions. We consider the two-dimensional case in presence of quenched disorder and use scale invariant scattering theory to determine all the…
The two-dimensional Ashkin-Teller model provides the simplest example of a statistical system exhibiting a line of critical points along which the critical exponents vary continously. The scaling limit of both the paramagnetic and…
We consider two critical semi-infinite subsystems with different critical exponents and couple them through their surfaces. The critical behavior at the interface, influenced by the critical fluctuations of the two subsystems, can be quite…
A missing piece is added to the Svetitsky-Yaffe conjecture. The spin model in the same universality class as the (2+1)d SU(4) theory, the 2d Ashkin-Teller model, has a line of continuously varying critical exponents. The exponents measured…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
The Ashkin-Teller (AT) model is a classic spin model in statistical mechanics. For traditional homogeneous lattices like triangular and kagome lattices, even when frustration exists, the model only has one ferromagnetic-paramagnetic…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
In planar lattice statistical mechanics models like coupled Ising with quartic interactions, vertex and dimer models, the exponents depend on all the Hamiltonian details. This corresponds, in the Renormalization Group language, to a line of…
We use a simple real-space renormalization group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary…
We show that equilibrium systems in $d$ dimension that obey the inequality $d\nu> 2,$ known as Harris criterion, exhibit suppressed energy fluctuation in their critical state. Ashkin-Teller model is an example in $d=2$ where the correlation…
The two-dimensional ferromagnetic anisotropic Ashkin-Teller model is investigated through a real-space renormalization-group approach. The critical frontier, separating five distinct phases, recover all the known exacts results for the…
Based on renormalization group arguments we establish that for a superconductor in the presence of a weak external magnetic field, $B$, the dependence on $B$ and the deviation from the critical temperature, $\tau$, of a thermodynamic…
The three-dimensional abelian Higgs model has been argued to be dual to a scalar field theory with a global U(1) symmetry. We show that this duality, together with the scaling and universality hypotheses, implies a scaling law for the…
Scalar field theories regularized on a $D$ dimensional lattice are found to exhibit double scaling for a class of critical behaviors labeled by an integer $m\geq 2$. The continuum theory reached in the double scaling limit defines a…
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts…
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple…
We perform a rigorous computation of the specific heat of the Ashkin-Teller model in the case of small interaction and we explain how the universality-nonuniversality crossover is realized when the isotropic limit is reached. We prove that,…