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

We calculate the critical exponent $\eta$ of the $D$-dimensional Ising modelfrom a simple truncation of the functional renormalization group flow equationsfor a scalar field theory with long-range interaction. Our approach relies onthe smallness of the inverse range of the interaction and on the assumptionthat the Ginzburg momentum defining the width of the scaling regime in momentumspace is larger than the scale where the renormalized interaction crosses overfrom long-range to short-range; the numerical value of $\eta$ can then beestimated by stopping the renormalization group flow at this scale. In threedimensions our result $\eta = 0.03651$ is in good agreement with recentconformal bootstrap and Monte Carlo calculations. We extend our calculations tofractional dimensions $D$ and obtain the resulting critical exponent $\eta(D)$between two and four dimensions. For dimensions $2\leq D \leq 3$ our result for$\eta$ is consistent with previous calculations.

Renormalization group for the $\varphi^4$-theory with long-range interaction and the critical exponent $\eta$ of the Ising model