dorsal/arxiv
View SchemaStability of 3D Cubic Fixed Point in Two-Coupling-Constant \phi^4-Theory
| Authors | H. Kleinert, S. Thoms, V. Schulte-Frohlinde |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9611050 |
| URL | https://arxiv.org/abs/quant-ph/9611050 |
| DOI | 10.1103/PhysRevB.56.14428 |
| Journal | Phys.Rev. B56 (1997) 14428 |
Abstract
For an anisotropic euclidean $\phi^4$-theory with two interactions $[u (\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4]$ the $\beta$-functions are calculated from five-loop perturbation expansions in $d=4-\varepsilon$ dimensions, using the knowledge of the large-order behavior and Borel transformations. For $\varepsilon=1$, an infrared stable cubic fixed point for $M \geq 3$ is found, implying that the critical exponents in the magnetic phase transition of real crystals are of the cubic universality class. There were previous indications of the stability based either on lower-loop expansions or on less reliable Pad\'{e approximations, but only the evidence presented in this work seems to be sufficently convincing to draw this conclusion.
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"abstract": "For an anisotropic euclidean $\\phi^4$-theory with two interactions $[u\n(\\sum_{i=1^M {\\phi}_i^2)^2+v \\sum_{i=1}^M \\phi_i^4]$ the $\\beta$-functions are\ncalculated from five-loop perturbation expansions in $d=4-\\varepsilon$\ndimensions, using the knowledge of the large-order behavior and Borel\ntransformations. For $\\varepsilon=1$, an infrared stable cubic fixed point for\n$M \\geq 3$ is found, implying that the critical exponents in the magnetic phase\ntransition of real crystals are of the cubic universality class. There were\nprevious indications of the stability based either on lower-loop expansions or\non less reliable Pad\\\u0027{e approximations, but only the evidence presented in\nthis work seems to be sufficently convincing to draw this conclusion.",
"arxiv_id": "quant-ph/9611050",
"authors": [
"H. Kleinert",
"S. Thoms",
"V. Schulte-Frohlinde"
],
"categories": [
"quant-ph",
"cond-mat",
"hep-th"
],
"doi": "10.1103/PhysRevB.56.14428",
"journal_ref": "Phys.Rev. B56 (1997) 14428",
"title": "Stability of 3D Cubic Fixed Point in Two-Coupling-Constant \\phi^4-Theory",
"url": "https://arxiv.org/abs/quant-ph/9611050"
},
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