Scaling region of the 3D Ising universality class in finite temperature QCD

Marianna Sorba; Michele Caselle

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Scaling region of the 3D Ising universality class in finite temperature QCD

Michele Caselle, Marianna Sorba

High Energy Physics - Lattice · Submitted 25 Nov 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The results we derive can be used as a sort of "reference frame" to chart the scaling region of the 3D Ising universality class.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.48 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.11 · mentions code or data availability 0.02.

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We introduce a universal combination of susceptibility and correlation length in the 3D Ising model, depending both on temperature and external magnetic field. Starting from a parametric representation of the equation of state, we study its behaviour close to the critical point. The results we derive can be used as a sort of "reference frame" to chart the scaling region of the 3D Ising universality class. More specifically, we focus on instances of Ising behaviour in finite temperature QCD and, among these, we are particularly interested on the critical ending point in the finite density, finite temperature QCD phase diagram. In this context, Monte Carlo simulations are not possible and it is particularly difficult to disentangle "magnetic-like" from "thermal-like" observables, thus an explicit charting of the critical region could be useful for a direct comparison of experimental results with QFT/Statmech predictions.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We introduce a universal combination of susceptibility and correlation length in the 3D Ising model, depending both on temperature and external magnetic field.	contribution 1.00	0.90	0.11	asserted 1.00
s1	Starting from a parametric representation of the equation of state, we study its behaviour close to the critical point.	method 0.92	0.89	0.03	asserted 0.91
s2	The results we derive can be used as a sort of "reference frame" to chart the scaling region of the 3D Ising universality class.	interpretation 0.81	0.80	0.44	asserted 0.57
s3	More specifically, we focus on instances of Ising behaviour in finite temperature QCD and, among these, we are particularly interested on the critical ending point in the finite density, finite temperature QCD phase diagram.	contribution 0.85	0.33	0.09	asserted 0.92
s4	In this context, Monte Carlo simulations are not possible and it is particularly difficult to disentangle "magnetic-like" from "thermal-like" observables, thus an explicit charting of the critical region could be useful for a direct comparison of experimental results with QFT/Statmech predictions.	background 0.46	0.10	0.09	hedged possibility 0.65

What kind of paper the classifier reports this is: theoretical result 0.67 · evidence from proof or derivation 1.00.

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Original abstract

We introduce a universal combination of susceptibility and correlation length in the 3D Ising model, depending both on temperature and external magnetic field. Starting from a parametric representation of the equation of state, we study its behaviour close to the critical point. The results we derive can be used as a sort of "reference frame" to chart the scaling region of the 3D Ising universality class. More specifically, we focus on instances of Ising behaviour in finite temperature QCD and, among these, we are particularly interested on the critical ending point in the finite density, finite temperature QCD phase diagram. In this context, Monte Carlo simulations are not possible and it is particularly difficult to disentangle "magnetic-like" from "thermal-like" observables, thus an explicit charting of the critical region could be useful for a direct comparison of experimental results with QFT/Statmech predictions.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 11 sentences without a confident label

Uses the method or tool of 3 papers

The coefficients $h_2n+1$ are fixed by means of a variational approach [ref] , and the polynomial is truncated up to the order that best fits the known values for the universal amplitude ratios.

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice · Parametric representation · 0.94
See [ref] for more details on this change of variables.

Charting the scaling region of the Ising universality class in two and three dimensions · Parametric representation · 0.83
The situation is solved by performing perturbative expansions around the exactly integrable directions $t=0$ and $H=0$ in the phase diagram [ref] , which correspond to the singular limits $η=0, ±∞$.

Ising field theory in a magnetic field: analytic properties of the free energy · Conclusions · 0.90

Uses data or values from 4 papers

Reliable estimates of the coefficients in the polynomial approximation of $h(θ)$ are obtained in [ref] up to the $7$-th order as [equation] and the smallest positive root is $θ_0^2=1.37861$.

25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice · Results · 0.99
Using the Monte Carlo value of $ξ_+/ξ_-$ [ref] we obtain $c=0.0416$ to be inserted in the parametric formula for the correlation length.

Universal amplitude ratios in the 3D Ising Universality Class · Results · 1.00
In these three limits the function $Ω$ can be written in terms of the standard universal amplitude ratios obtained with remarkable precision in Monte Carlo simulations [ref] $Q_2=1.207(2)$, $Γ_+/Γ_-=4.714(4)$, and $ξ_+/ξ_-=1.896(3)$ as [equation] We then have numerically $Ω(-∞)=1$, $Ω(0)=1.25(11)$, and $Ω(+∞)=1.355(71)$.

Universal Amplitude Ratios in the 3D Ising Model · 3D Ising model and observable $Ω$ · 1.00

Cites as background 2 papers

From conformal perturbation and bootstrap [ref] , several results are known on the behaviour of the model in three dimensions at the critical point or when a single perturbing operator is present.

Precision Islands in the Ising and $O(N)$ Models · Introduction · 0.96
We refer to [ref] for an exhaustive discussion about the derivation of the universal function $Ω$ also in the bidimensional Ising model.

Charting the scaling region of the Ising universality class in two and three dimensions · Conclusions · 0.88

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