Fisher zeros
E911213
Fisher zeros are the complex-temperature zeros of a statistical mechanical partition function that characterize phase transitions and critical behavior in finite systems.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
concept in statistical mechanics
ⓘ
mathematical object ⓘ |
| alsoKnownAs | Fisher zeroes ⓘ |
| appearIn | complex analysis of partition functions ⓘ |
| appliesTo | finite systems ⓘ |
| approach | real temperature axis in the thermodynamic limit ⓘ |
| associatedWith |
non-analyticity of free energy
ⓘ
singularities in thermodynamic functions ⓘ |
| characterizes |
critical behavior
ⓘ
phase transitions ⓘ |
| definedAs | zeros of the partition function in the complex temperature plane ⓘ |
| definedOn | complex temperature plane ⓘ |
| distributionDetermines |
location of critical points
ⓘ
order of phase transition ⓘ |
| field |
critical phenomena
ⓘ
phase transition theory ⓘ statistical mechanics ⓘ |
| generalizationOf | real-temperature singularity analysis ⓘ |
| historicalContext | introduced in the study of critical phenomena in the 1960s ⓘ |
| influence | analytic continuation of thermodynamic quantities ⓘ |
| limitBehavior | condense into curves or areas in the thermodynamic limit ⓘ |
| mathematicalNature | complex roots of an analytic function ⓘ |
| namedAfter | Michael E. Fisher NERFINISHED ⓘ |
| parameterizedBy |
complex coupling constant
ⓘ
complex inverse temperature ⓘ |
| relatedConcept |
Fisher edge singularity
ⓘ
Fisher renormalization ⓘ Lee–Yang circle theorem NERFINISHED ⓘ |
| relatedTo |
Lee–Yang zeros
NERFINISHED
ⓘ
Yang–Lee theory NERFINISHED ⓘ partition function zeros ⓘ |
| studiedUsing |
Monte Carlo simulations
ⓘ
exactly solvable models ⓘ series expansions ⓘ transfer matrix methods ⓘ |
| topologyOf | zero locus in complex temperature plane ⓘ |
| usedFor |
extrapolating finite-size data to the thermodynamic limit
ⓘ
locating pseudo-critical points in finite systems ⓘ |
| usedIn |
Ising model analysis
ⓘ
Potts model analysis ⓘ finite-size scaling analysis ⓘ lattice models ⓘ numerical studies of phase transitions ⓘ spin systems ⓘ |
| usedToDetermine |
critical exponents
ⓘ
critical temperature ⓘ universality class ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.