Related papers: Curvature function renormalisation, topological ph…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase…
We apply the non-perturbative renormalization group method to a class of out-of-equilibrium phase transitions (usually called ``parity conserving'' or, more properly, ``generalized voter'' class) which is out of the reach of perturbative…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing…
Critical transition points between symmetry-broken phases are characterized as fixed points in the renormalization group (RG) theory. We show that, following the standard Wilsonian procedure that traces out the large momentum modes, this…
The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3<d<4, with a…
We find the cross-over behavior for the spin-spin correlation function for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation approach of the perturbation series…
We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
At criticality, discrete quantum-gravity models are expected to give rise to continuum spacetime. Recent progress has established the functional renormalization group method in the context of such models as a practical tool to study their…
Two and three point functions of composite operators are analysed with regard to (logarithmically) divergent contact terms. Using the renormalisation group of dimensional regularisation it is established that the divergences are governed by…
We study renormalization group multicritical fixed points in the $\epsilon$-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group $H_N$. After reviewing the algebra of $H_N$-invariant polynomials…
A general ansatz in Renormalization Theory, already established in many important situations, states that exponential convergence of renormalization orbits implies that topological conjugacies are actually smooth (when restricted to the…
Topological gapless phases of matter have been a recent interest among theoretical and experimental condensed matter physicists. Fermionic chains with extended nearest neighbor couplings have been observed to show unique topological…
The observation of critical-like behavior in cortical networks represents a major step forward in elucidating how the brain manages information. Understanding the origin and functionality of critical-like dynamics, as well as their…
Background: Quantum Chromodynamics is expected to have a phase transition in the same static universality class as the 3D Ising model and the liquid-gas phase transition. The properties of the equation of state, the transport coefficients,…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
Topological phase transitions can be described by the theory of critical phenomena and identified by critical exponents that define their universality classes. This is a consequence of the existence of a diverging length at the transition…
Renormalization schemes and cutoff schemes allow for the introduction of various distinct renormalization scales for distinct couplings. We consider the coupled renormalization group flow of several marginal couplings which depend on just…