{"title":"Is directed percolation class for synchronization transition robust with multi-site interactions?","authors":"Manoj C. Warambhe, Prashant M. Gade","doi":"10.1140/epjb/s10051-025-00928-z","DOIUrl":null,"url":null,"abstract":"<p>Coupled map lattice with pairwise local interactions is a well-studied system. However, in several situations, such as neuronal or social networks, multi-site interactions are possible. In this work, we study the coupled Gauss map in one dimension with 2-site, 3-site, 4-site and 5-site interaction. This coupling cannot be decomposed in pairwise interactions. We coarse-grain the variable values by labeling the sites above <span>\\(x^{\\star }\\)</span> as up spin (+ 1) and the rest as down spin (– 1) where <span>\\(x^{\\star }\\)</span> is the fixed point. We define flip rate <i>F</i>(<i>t</i>) as the fraction of sites <i>i</i> such that <span>\\(s_{i}(t-1) \\ne s_{i}(t)\\)</span> and persistence <i>P</i>(<i>t</i>) as the fraction of sites <i>i</i> such that <span>\\(s_{i}(t')=s_{i}(0)\\)</span> for all <span>\\(t' \\le t\\)</span>. The dynamic phase transitions to a synchronized state is studied above quantifiers. For 3 and 5 sites interaction, we find that at the critical point, <span>\\(F(t) \\sim t^{-\\delta }\\)</span> with <span>\\(\\delta =0.159\\)</span> and <span>\\(P(t) \\sim t^{-\\theta }\\)</span> with <span>\\(\\theta =1.5\\)</span>. They match the directed percolation (DP) class. Finite-size and off-critical scaling is consistent with DP class. For 2 and 4 site interactions, the exponent <span>\\(\\delta \\)</span> and behavior of <i>P</i>(<i>t</i>) at critical point changes. Furthermore, we observe logarithmic oscillations over and above power-law decay at the critical point for 4-site coupling. Thus multi-site interactions can lead to new universality class(es).</p>","PeriodicalId":787,"journal":{"name":"The European Physical Journal B","volume":"98 4","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal B","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjb/s10051-025-00928-z","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
引用次数: 0
Abstract
Coupled map lattice with pairwise local interactions is a well-studied system. However, in several situations, such as neuronal or social networks, multi-site interactions are possible. In this work, we study the coupled Gauss map in one dimension with 2-site, 3-site, 4-site and 5-site interaction. This coupling cannot be decomposed in pairwise interactions. We coarse-grain the variable values by labeling the sites above \(x^{\star }\) as up spin (+ 1) and the rest as down spin (– 1) where \(x^{\star }\) is the fixed point. We define flip rate F(t) as the fraction of sites i such that \(s_{i}(t-1) \ne s_{i}(t)\) and persistence P(t) as the fraction of sites i such that \(s_{i}(t')=s_{i}(0)\) for all \(t' \le t\). The dynamic phase transitions to a synchronized state is studied above quantifiers. For 3 and 5 sites interaction, we find that at the critical point, \(F(t) \sim t^{-\delta }\) with \(\delta =0.159\) and \(P(t) \sim t^{-\theta }\) with \(\theta =1.5\). They match the directed percolation (DP) class. Finite-size and off-critical scaling is consistent with DP class. For 2 and 4 site interactions, the exponent \(\delta \) and behavior of P(t) at critical point changes. Furthermore, we observe logarithmic oscillations over and above power-law decay at the critical point for 4-site coupling. Thus multi-site interactions can lead to new universality class(es).