English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper we give a complete analysis of the phase transitions in themean-field Blume-Emery-Griffiths lattice-spin model with respect to thecanonical ensemble, showing both a second-order, continuous phase transitionand a first-order, discontinuous phase transition for appropriate values of thethermodynamic parameters that define the model. These phase transitions areanalyzed both in terms of the empirical measure and the spin per site bystudying bifurcation phenomena of the corresponding sets of canonicalequilibrium macrostates, which are defined via large deviation principles.Analogous phase transitions with respect to the microcanonical ensemble arealso studied via a combination of rigorous analysis and numerical calculations.Finally, probabilistic limit theorems for appropriately scaled values of thetotal spin are proved with respect to the canonical ensemble. These limittheorems include both central-limit-type theorems, when the thermodynamicparameters are not equal to critical values, and noncentral-limit-typetheorems, when these parameters equal critical values.

Analysis of phase transitions in the mean-field Blume–Emery–Griffiths model