Critical Phenomena and Renormalization-Group Theory¶
Pelissetto, A., & Vicari, E. (2002). Critical Phenomena and Renormalization-Group Theory. Physics Reports, 368(6), 549-727.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Universality in Critical Phenomena
- Formal case — liquid-gas and uniaxial ferromagnet share the 3D Ising class:
This sourceMonumental precision review of critical exponents (Ising, XY, Heisenberg, percolation); confirms experimentally-measured universality to high accuracy. Cites Lipa et al. 2003 and confirms helium-4 lambda-transition data.
Supported in partVerified against the work's full text
Supplies the qualitative typology of the Ising class (liquid-vapor, multicomponent fluid mixtures, uniaxial magnetic systems) but not the quoted exponents or the upper-critical-dimension sentence.
“Ind eed, many systems characterized by short-range interactions and a scalar order parameter undergo a critica l transition belonging to the Ising universality class. We mention the liquid-vapor transition in simple fluids, the transitions in multicomponent fluid mixtures, in uniaxial antiferromagnetic materials, and in micellar sys tems (see Sec. 3.1.1).”
- Formal case — liquid-gas and uniaxial ferromagnet share the 3D Ising class:
Mechanisms¶
- High-Temperature Series Resummation
- Its strength is that decades of universality knowledge — that whole classes of systems share the same critical exponents — become a lever that turns a modest high-temperature series into a sharp critical estimate.
This sourceReviews universality classes that share critical exponents and shows how high-temperature series analyses can yield precise critical estimates when constrained by established scaling knowledge.
- Its strength is that decades of universality knowledge — that whole classes of systems share the same critical exponents — become a lever that turns a modest high-temperature series into a sharp critical estimate.
Verification¶
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