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We determine the critical coupling in the continuum limit employing the tensor network formulation for scalar field theories proposed in our previous paper. We obtain $\\left[ \\lambda / \\mu_{\\mathrm{c}}^{2} \\right]_{\\mathrm{cont.}} = 10.913(56)$ with the quartic coupling $\\lambda$ and the renormalized cr"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.12376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-lat","submitted_at":"2018-11-29T18:39:59Z","cross_cats_sorted":[],"title_canon_sha256":"b54e43795a562337ec419450bcd6d3aa0fce61f55399aba61227cf366c16d699","abstract_canon_sha256":"cb28945782992a61d416431c6fac3b8cca4bb03fa355a802382a356c4ea8527e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:26.141770Z","signature_b64":"XiMu0hQkD/xYkmcmBPixYAAcvRLx0rIRA23RTRCeZmzvmiSaPqnDTnfbKW2WyeZ+p1493VvRsKD5vEv+C6RfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cf28bd68b6e81df3a83c77d9a8ed2da1dde889152f47ae31c6ceab81d3b05ac","last_reissued_at":"2026-05-17T23:42:26.141016Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:26.141016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tensor network analysis of critical coupling in two dimensional $\\phi^{4}$ theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Daisuke Kadoh, Ryo Sakai, Shinji Takeda, Yoshifumi Nakamura, Yoshinobu Kuramashi, Yusuke Yoshimura","submitted_at":"2018-11-29T18:39:59Z","abstract_excerpt":"We make a detailed analysis of the spontaneous $Z_{2}$-symmetry breaking in the two dimensional real $\\phi^{4}$ theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the physical observables without statistical uncertainties. 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