In the past decades considerable efforts have been made in orderto understand the critical features of long-range interacting models, i.e. those where the couplings decay algebraically as r^(\u2212d\u2212\u03c3) with\u03c3 >0. According to the well-established Sak\u2019s criterion for O(N) models, the short-range critical behavior survives up to a given \u03c3\u2217\u22642. However, the applicability of this picture to describe the the two dimensional classical XY model is complicated by the the presence, in the short-range regime, of a line of RG fixed points,which gives rise to the celebrated Berezinskii – Kosterlitz – Thouless (BKT) phenomenology. Our recent field-theoretical analysis finds there is not a specific, temperature-independent, value of \u03c3\u2217: while for \u03c3 <7\/4 the BKT fixed line vanishes and we have an order-disorder transition, for 7\/4< \u03c3 <2 we have both a low-temperature broken phase and an intermediate quasi-ordered one. In this regime we were able to full characterize the critical properties of this new transition.<\/p>\n","protected":false},"excerpt":{"rendered":"
In the past decades considerable efforts have been made in orderto understand the critical features of long-range interacting models, i.e. those where the couplings decay algebraically as r^(\u2212d\u2212\u03c3) with\u03c3 >0. According to the well-established Sak\u2019s criterion for O(N) models, the short-range critical behavior survives up to a given \u03c3\u2217\u22642. However, the applicability of this picture to describe the the two dimensional classical XY model is complicated by the the presence, in the short-range regime, of a line of RG fixed points,which gives rise to the celebrated Berezinskii – Kosterlitz – Thouless (BKT) phenomenology. Our recent field-theoretical analysis finds there is not a specific, temperature-independent, value of \u03c3\u2217: while for \u03c3 <7\/4 the BKT fixed line vanishes and we have an order-disorder transition, for 7\/4< \u03c3 <2 we have both a low-temperature broken phase and an intermediate quasi-ordered one. In this regime we were able to full characterize the critical properties of this new transition.<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_uag_custom_page_level_css":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[6],"tags":[],"class_list":["post-676","post","type-post","status-publish","format-standard","hentry","category-fomo2021-abstract"],"jetpack_featured_media_url":"","uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"ashe-slider-full-thumbnail":false,"ashe-full-thumbnail":false,"ashe-list-thumbnail":false,"ashe-grid-thumbnail":false,"ashe-single-navigation":false},"uagb_author_info":{"display_name":"Cretan Matterwaves","author_link":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/author\/bec\/"},"uagb_comment_info":0,"uagb_excerpt":"In the past decades considerable efforts have been made in orderto understand the critical features of long-range interacting models, i.e. those where the couplings decay algebraically as r^(\u2212d\u2212\u03c3) with\u03c3 >0. According to the well-established Sak\u2019s criterion for O(N) models, the short-range critical behavior survives up to a given \u03c3\u2217\u22642. However, the applicability of this picture…","jetpack_sharing_enabled":true,"publishpress_future_action":{"enabled":false,"date":"2026-07-29 19:57:40","action":"category","newStatus":"draft","terms":[],"taxonomy":"category","extraData":[]},"publishpress_future_workflow_manual_trigger":{"enabledWorkflows":[]},"_links":{"self":[{"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/posts\/676","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/comments?post=676"}],"version-history":[{"count":1,"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/posts\/676\/revisions"}],"predecessor-version":[{"id":679,"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/posts\/676\/revisions\/679"}],"wp:attachment":[{"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/media?parent=676"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/categories?post=676"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.matterwaveoptics.eu\/FOMO2022\/wp-json\/wp\/v2\/tags?post=676"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}