Related papers: The D=1 Matrix Model and the Renormalization Group

We adapt White's density matrix renormalisation group (DMRG) to the direct study of critical phenomena. We use the DMRG to generate transformations in the space of coupling constants. We postulate that a study of density matrix eigenvalues…

In previous studies, we proposed a scaling ansatz for electron-electron interactions under renormalization group transformation. With the inclusion of phonon-mediated interactions, we show that the scaling ansatz, characterized by the…

The requirement that duality and renormalization group transformations commute as motions in the space of a theory has recently been explored to extract information about the renormalization flows in different statistical and field…

The field-theoretical renormalization group approach in three dimensions is used to estimate the universal critical values of renormalized coupling constants g_6 and g_8 for the O(n)-symmetric model. The RG series for g_6 and g_8 are…

The general prescription for constructing the continuum limit of a field theory is explained using Wilson's renormalization group. We then formulate the renormalization group in perturbation theory and apply it to the four dimensional phi4…

In statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in…

In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…

We establish a renormalization group approach which is implemented on the degrees of freedom defined by the overlap of two replicas to determine the critical fixed point and to extract four critical exponents for the phase transition of the…

We apply the density matrix renormalization group (DMRG) method to a non-equilibrium problem: the asymmetric exclusion process in one dimension. We study the stationary state of the process to calculate the particle density profile…

We show that it is possible to use dimensional regularization (DR) beyond the usual $\varepsilon$-expansion in the context of renormalization group (RG) calculations in Critical Phenomena. Based on this fact, we propose a new functional RG…

The structure of the UV divergencies in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergencies (asymptotics)…

A derivative expansion of the effective average action beyond first order yields renormalization group functional flow equations which are used for the computation of critical exponents of the Ising universality class. The critical exponent…

We use a renormalization group method, similar to that developed for random spin chains, to infer information about the layouts of cellular wireless networks.

Using the recent six loop renormalization group functions for Lee-Yang and percolation theory constructed by Schnetz from a scalar cubic Lagrangian, we deduce the $\epsilon$ expansion of the critical exponents for both cases. Estimates for…

The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this…

Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…

Guided by critical systems found in nature we develop a novel mechanism consisting of inhomogeneous polynomial regularisation via which we can induce scale invariance in deep learning systems. Technically, we map our deep learning (DL)…

Critical pair analysis provides a convenient and computable criterion of confluence, which is a fundamental property in rewriting theory, for a wide variety of rewriting systems. Bonchi et al. showed validity of critical pair analysis for…

We revisit the perturbative S-matrix of c=1 string theory from the worldsheet perspective. We clarify the origin of the leg pole factors, the non-analyticity of the string amplitudes, and the validity as well as limitations of earlier…

We argue that string theory should have a formulation for which stability and causality are evident. Rather than regard strings as fundamental objects, we suggest they should be regarded as composite systems of more fundamental point-like…