Corrections to finite-size scaling in the 3D Ising model based on nonperturbative approaches and Monte Carlo simulations

Abstract

Corrections to scaling in the 3D Ising model are studied based on non-perturbative analytical arguments and Monte Carlo (MC) simulation data for different lattice sizes L. Analytical arguments show the existence of corrections with the exponent (γ − 1)/ν ≈ 0.38, the leading correction-to-scaling exponent being ω ≤ (γ − 1)/ν. A numerical estimation of ω from the susceptibility data within 40 ≤ L ≤ 2048 yields ω = 0.25(33). It is consistent with the statement ω ≤ (γ − 1)/ν, as well as with the value ω = 1/8 of the GFD theory. We reconsider the MC estimation of ω from smaller lattice sizes to show that it does not lead to conclusive results, since the obtained values of ω depend on the particular method chosen. In particular, estimates ranging from ω = 1.274(72) to ω = 0.18(37) are obtained by four different finite-size scaling methods, using MC data for thermodynamic average quantities, as well as for partition function zeros. We discuss the influence of ω on the estimation of exponents η and ν.

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

“…The systematical errors of these approximation techniques are related directly to the physical conceptions/pictures at the first beginning and the neglects of important non-locality factors during procedures. As pointed out in [30] that these estimates in [17] were obtained based on certain hypotheses (e.g., the existence of a sharp kink) and that if these hypotheses are not used, then the conformal bootstrap analysis appears to be consistent with the values η = 1/8 and ν = 2/3, obtained by Grouping of Feynman Diagrams, which are consistent with the Zhang's solutions obtained in [3]. Furthermore, Zhang's results agree with some experimental results, which are carefully performed with high accuracy (see in [31], for instance).…”

“…Furthermore, Zhang's results agree with some experimental results, which are carefully performed with high accuracy (see in [31], for instance). After its publication [3], Zhang's conjectured solution has received supports from several groups, for instance, March and his co-workers [32][33][34][35][36], Ławrynowicz and some mathematicians [6,7,37,38], Kaupuzs and his colleagues [30,39,40], and others [41][42][43][44][45][46][47][48][49][50][51][52][53]. In [8], Zhang-Suzuki-March rigorously proved four Theorems, which verifies the correctness of the Zhang's conjectured solution [3].…”

Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics

“…Starting from generalized versions of the master equation, one has to construct an efficient procedure for calculating memory kernels, including non-Markovian cases [218]. Nonperturbative approaches [219][220][221][222] can provide here superior efficiency and accuracy improvements, see, e.g., [223] where they were tested on the Fenna-Matthews-Olson (FMO) light-harvesting complexes important in the analysis of photosynthetic systems [224][225][226][227]. The problems of reductions of Mori-Zwanzig theory models (not limited to their quantum-classical versions) have been a topic of discussion which included also relevant computational complexity issues [228].…”

Activating critical exponent spectra with a slow drive

“…However, universality extends beyond these so-called relevant exponents to an entire spectrum of universal exponents [1][2][3]. Yet, this fully universal information is not easily accessible in static experiments (see, e.g., [2,[4][5][6]), or even numerics, the subleading character of the associated power laws is easily overwritten by the more dominant exponents (see, e.g., [7][8][9][10][11][12][13][14]). Exceptions to this scenario are available in conformal field theories, where a relation between the scaling dimensions of operators and the energy spectrum has been established [15][16][17][18] as well as in transitions with dangerously irrelevant parameters, where specific exponents are accessible [19].…”