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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Fekete's lemma shows the existence of limits in subadditive sequences. Thislemma, and generalisations of it, also have been used to prove the existence ofthermodynamic limits in statistical mechanics. In this paper it is shown thatthe two variable supermultiplicative relation $$ p_{n_1}(m_1)\,p_{n_2}(m_2)\leq p_{n_1+n_2}(m_1 + m_2) $$ together with mild assumptions, imply theexistence of the limit $$ \log \mathcal{P}_\#(\epsilon) = \lim_{n\to\infty}\frac{1}{n} \log p_n(\lfloor \epsilon n \rfloor).$$ This is a generalisation ofFekete's lemma. The existence of $\mathcal{P}_\#(\epsilon)$ are proven formodels of adsorbing walks and polygons, and for pulled polygons. In addition,numerical data are presented estimating the general shape of $\log\mathcal{P}_\# (\epsilon)$ of models of square lattice self-avoiding walks andpolygons.

Supermultiplicative relations in models of interacting self-avoiding walks and polygons