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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Fisher zeros canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11205541 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fisher zeros Context triple: [Yang–Lee theory, relatedTo, Fisher zeros]
-
A.
Hardy Z-function
The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
-
B.
Ginibre ensemble
The Ginibre ensemble is a fundamental class of non-Hermitian random matrices with independently distributed complex (or real/quaternion) Gaussian entries, widely studied for its rich eigenvalue statistics in random matrix theory.
-
C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
-
D.
Hurwitz determinants
Hurwitz determinants are specific determinants constructed from a polynomial’s coefficients that are used to test whether all roots of the polynomial lie in the left half of the complex plane, thereby assessing system stability.
-
E.
Voronin universality theorem
The Voronin universality theorem is a result in analytic number theory stating that, in a precise sense, the Riemann zeta function can approximate any non-vanishing analytic function arbitrarily well on certain regions of the complex plane.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Fisher zeros Target entity description: Fisher zeros are the complex-temperature zeros of a statistical mechanical partition function that characterize phase transitions and critical behavior in finite systems.
-
A.
Hardy Z-function
The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
-
B.
Ginibre ensemble
The Ginibre ensemble is a fundamental class of non-Hermitian random matrices with independently distributed complex (or real/quaternion) Gaussian entries, widely studied for its rich eigenvalue statistics in random matrix theory.
-
C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
-
D.
Hurwitz determinants
Hurwitz determinants are specific determinants constructed from a polynomial’s coefficients that are used to test whether all roots of the polynomial lie in the left half of the complex plane, thereby assessing system stability.
-
E.
Voronin universality theorem
The Voronin universality theorem is a result in analytic number theory stating that, in a precise sense, the Riemann zeta function can approximate any non-vanishing analytic function arbitrarily well on certain regions of the complex plane.
- F. None of above. chosen
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 ⓘ |
| parameterizedBy |
complex coupling constant
ⓘ
complex inverse temperature ⓘ |
| relatedConcept |
Fisher edge singularity
ⓘ
Fisher renormalization ⓘ Lee–Yang circle theorem ⓘ |
| relatedTo |
Lee–Yang zeros
ⓘ
linked to:
Yang–Lee theory
Yang–Lee theory ⓘ 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Fisher zeros Description of subject: Fisher zeros are the complex-temperature zeros of a statistical mechanical partition function that characterize phase transitions and critical behavior in finite systems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.