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

We investigate the potential energy surface of a phi^4 model with infiniterange interactions. All stationary points can be uniquely characterized bythree real numbers $\alpha_+, alpha_0, alpha_- with alpha_+ + alpha_0 + alpha_-= 1, provided that the interaction strength mu is smaller than a criticalvalue. The saddle index n_s is equal to alpha_0 and its distribution functionhas a maximum at n_s^max = 1/3. The density p(e) of stationary points withenergy per particle e, as well as the Euler characteristic chi(e), are singularat a critical energy e_c(mu), if the external field H is zero. However, e_c(mu)\neq upsilon_c(mu), where upsilon_c(mu) is the mean potential energy perparticle at the thermodynamic phase transition point T_c. This proves thatprevious claims that the topological and thermodynamic transition pointscoincide is not valid, in general. Both types of singularities disappear for H\neq 0. The average saddle index bar{n}_s as function of e decreasesmonotonically with e and vanishes at the ground state energy, only. Incontrast, the saddle index n_s as function of the average energy bar{e}(n_s) isgiven by n_s(bar{e}) = 1+4bar{e} (for H=0) that vanishes at bar{e} = -1/4 >upsilon_0, the ground state energy.Comment: 9 PR pages, 6 figure

physical review. e, statistical, nonlinear and soft matter physics

Saddle index properties, singular topology, and its relation to thermodynamic singularities for a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math>mean-field model

Saddle index properties, singular topology, and its relation to thermodynamic singularities for aϕ4mean-field model