On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late

On the Finite-Temperature Generalization of the C-theorem and the Interplay between Classical and Quantum Fluctuations

The behavior of the finite-temperature C-function, defined by Neto and Fradkin [Nucl. Phys. B {\bf 400}, 525 (1993)], is analyzed within a d -dimensional exactly solvable lattice model, recently proposed by Vojta [Phys. Rev. B {\bf 53}, 710 (1996)], which is of the same universality class as the quantum nonlinear O(n) sigma model in the limit $n\to \infty$. The scaling functions of C for the cases d=1 (absence of long-range order), d=2 (existence of a quantum critical point), d=4 (existence of a line of finite temperature critical points that ends up with a quantum critical point) are derived and analyzed. The locations of regions where C is monotonically increasing (which depend significantly on d) are exactly determined. The results are interpreted within the finite-size scaling theory that has to be modified for d=4. PACS number(s): 05.20.-y, 05.50.+q, 75.10.Hk, 75.10.Jm, 63.70.+h, 05.30-d, 02.30Comment: 15 pages LATEX, ioplppt.sty file used, 6 EPS figures. Some changes made in section V (on finite-size scaling interpretation of the results obtained

Exact Three Dimensional Casimir Force Amplitude, CC-function and Binder's Cumulant Ratio: Spherical Model Results

The three dimensional mean spherical model on a hypercubic lattice with a film geometry $L\times \infty ^2$ under periodic boundary conditions is considered in the presence of an external magnetic field $H$. The universal Casimir amplitude $\Delta$ and the Binder's cumulant ratio $B$ are calculated exactly and found to be $\Delta =-2\zeta (3)/(5\pi)\approx -0.153051$ and $B=2\pi /(\sqrt{5}\ln ^3[(1+\sqrt{5})/2]).$ A discussion on the relations between the finite temperature $C$-function, usually defined for quantum systems, and the excess free energy (due to the finite-size contributions to the free energy of the system) scaling function is presented. It is demonstrated that the $C$-function of the model equals 4/5 at the bulk critical temperature $T_c$. It is analytically shown that the excess free energy is a monotonically increasing function of the temperature $T$ and of the magnetic field $|H|$ in the vicinity of $T_c.$ This property is supposed to hold for any classical $d$-dimensional $O(n),n>2,$ model with a film geometry under periodic boundary conditions when $d\leq 3$. An analytical evidence is also presented to confirm that the Casimir force in the system is negative both below and in the vicinity of the bulk critical temperature $T_c.$Comment: 12 pages revtex, one eps figure, submitted to Phys. Rev E A set of references added with the text needed to incorporate them. Small changes in the title and in the abstrac

BLOOM: A 176B-Parameter Open-Access Multilingual Language Model

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License

Theory of critical phenomena in finite-size systems: scaling and quantum effects

The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveal