arXiv subjects

Martin Weigel

Publications and source records attributed to Martin Weigel.

78 records · Page 5Linked to original sources

arXiv2004

The Harris-Luck criterion for random lattices

The Harris-Luck criterion judges the relevance of (potentially) spatially correlated, quenched disorder induced by, e.g., random bonds, randomly diluted sites or a quasi-periodicity of the lattice, for altering the critical behavior of a coupled matter system. We investigate the applicability of this type of criterion to the case of spin variables coupled to random lattices. Their aptitude to alter critical behavior depends on the degree of spatial correlations present, which is quantified by a wandering exponent. We consider the cases of Poissonian random graphs resulting from the Voronoi-Delaunay construction and of planar, ``fat'' $ϕ^3$ Feynman diagrams and precisely determine their wandering exponents. The resulting predictions are compared to various exact and numerical results for the Potts model coupled to these quenched ensembles of random graphs.

cond-mat.stat-mech↗

arXiv2001

Random-cluster multi-histogram sampling for the q-state Potts model

Using the random-cluster representation of the $q$-state Potts models we consider the pooling of data from cluster-update Monte Carlo simulations for different thermal couplings $K$ and number of states per spin $q$. Proper combination of histograms allows for the evaluation of thermal averages in a broad range of $K$ and $q$ values, including non-integer values of $q$. Due to restrictions in the sampling process proper normalization of the combined histogram data is non-trivial. We discuss the different possibilities and analyze their respective ranges of applicability.

cond-mat.stat-mech↗

arXiv2000

Universal amplitude ratios in finite-size scaling: three-dimensional Ising model

Motivated by the results of two-dimensional conformal field theory (CFT) we investigate the finite-size scaling of the mass spectrum of an Ising model on three-dimensional lattices with a spherical cross section. Using a cluster-update Monte Carlo technique we find a linear relation between the masses and the corresponding scaling dimensions, in complete analogy to the situation in two dimensions. Amplitude ratios as well as the amplitudes themselves appear to be universal in this case.

cond-mat.stat-mech↗

arXiv2000

Universal amplitude-exponent relation for the Ising model on sphere-like lattices

Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems $S^{d-1}\times\mathbb{R}$ of arbitrary dimensionality $d$. Numerical studies have up to now been unable to validate this result due to the intricacies of lattice discretisation of such curved spaces. We present a cluster-update Monte Carlo study of the Ising model on a three-dimensional geometry using slightly irregular lattices that confirms the validity of a linear amplitude-exponent relation to high precision.

cond-mat.stat-mech↗

arXiv2000

Monte Carlo study of the scaling of universal correlation lengths in three-dimensional O(n) spin models

Using an elaborate set of simulational tools and statistically optimized methods of data analysis we investigate the scaling behavior of the correlation lengths of three-dimensional classical O($n$) spin models. Considering three-dimensional slabs $S^1\times S^1\times\mathbb{R}$, the results over a wide range of $n$ indicate the validity of special scaling relations involving universal amplitude ratios that are analogous to results of conformal field theory for two-dimensional systems. A striking mismatch of the $n\to\infty$ extrapolation of these simulations against analytical calculations is traced back to a breakdown of the identification of this limit with the spherical model.

cond-mat.stat-mech↗

arXiv1998

Universal amplitudes in the FSS of three-dimensional spin models

In a MC study using a cluster update algorithm we investigate the finite-size scaling (FSS) of the correlation lengths of several representatives of the class of three-dimensional classical O(n) symmetric spin models on a column geometry. For all considered models we find strong evidence for a linear relation between FSS amplitudes and scaling dimensions when applying antiperiodic instead of periodic boundary conditions across the torus. The considered type of scaling relation can be proven analytically for systems on two-dimensional strips with periodic bc using conformal field theory

cond-mat.stat-mech↗