Three dimensional massive scalar field theory and the derivative expansion of the renormalization group

Tim R. Morris

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Three dimensional massive scalar field theory and the derivative expansion of the renormalization group

Tim R. Morris

High Energy Physics - Theory · Submitted 11 Dec 1996

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

The authors' main claim We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum -- without using bare actions or any tuning procedure.

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arXiv IDhep-th/9612117 (version 3)

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CitationTim R. Morris. "Three dimensional massive scalar field theory and the derivative expansion of the renormalization group." arXiv:hep-th/9612117 (1996). https://pith.science/paper/R5EAKGOY

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,398 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.80 · states limitation 0.92 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.24 · compares with prior results 0.98 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum -- without using bare actions or any tuning procedure. As an example, we estimate the universal couplings of the non-perturbative three-dimensional one-component massive scalar field theory in the Ising model universality class, by using a derivative expansion (and no other approximation). These are compared to the recent results from other methods. At order derivative-squared approximation, the four-point coupling at zero momentum is better determined by other methods, but factoring this out appropriately, all our other results are in very close agreement with the most powerful of these methods. In addition we provide for the first time, estimates of the n-point couplings at zero momentum, with n=12,14, and the order momentum-squared parts with n=2 ... 10.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum -- without using bare actions or any tuning procedure.	contribution 0.85	0.95	0.76	asserted 1.00
s1	As an example, we estimate the universal couplings of the non-perturbative three-dimensional one-component massive scalar field theory in the Ising model universality class, by using a derivative expansion (and no other approximation).	contribution 0.74	0.96	0.16	asserted 0.89
s2	These are compared to the recent results from other methods.	result 0.46	0.36	0.04	asserted 0.81
s3	At order derivative-squared approximation, the four-point coupling at zero momentum is better determined by other methods, but factoring this out appropriately, all our other results are in very close agreement with the most powerful of these methods.	result 0.54	0.84	0.23	asserted 1.00
s4	In addition we provide for the first time, estimates of the n-point couplings at zero momentum, with n=12,14, and the order momentum-squared parts with n=2 ... 10.	contribution 0.67	0.96	0.10	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.60 · evidence from simulation or computation 0.79.

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arXiv listing abstract v3

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Original abstract

We show that non-perturbative fixed points of the exact renormalization group, their perturbations and corresponding massive field theories can all be determined directly in the continuum -- without using bare actions or any tuning procedure. As an example, we estimate the universal couplings of the non-perturbative three-dimensional one-component massive scalar field theory in the Ising model universality class, by using a derivative expansion (and no other approximation). These are compared to the recent results from other methods. At order derivative-squared approximation, the four-point coupling at zero momentum is better determined by other methods, but factoring this out appropriately, all our other results are in very close agreement with the most powerful of these methods. In addition we provide for the first time, estimates of the n-point couplings at zero momentum, with n=12,14, and the order momentum-squared parts with n=2 ... 10.

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References

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Asymptotic behaviour of the derivative expansion in the ERG
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The derivative expansion of the exact renormalization group is divergent for generic operators in any dimension, but behaves as an asymptotic series that converges to high order in common applications.
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By combining the exact renormalization group flow with the modified split Ward identity in conformally reduced gravity, the authors derive a unique background-independent scale under which the flow equations become in...
On the number of relevant operators in asymptotically safe gravity
hep-th 2013-01 conditional novelty 6.0 of 10

Assuming a non-trivial ultraviolet fixed point exists in the f(R) approximation of gravity's functional renormalization group, the number of relevant directions is shown to be finite.
Asymptotic safety in the f(R) approximation
hep-th 2012-11 conditional novelty 6.0 of 10

The f(R) truncation of asymptotically safe gravity admits lines of fixed points with a continuous, non-quantized spectrum of operator dimensions, which the authors argue rules out this truncation as a predictive framework.
Fundamentals of the Exact Renormalization Group
hep-th 2010-03 conditional novelty 6.0 of 10

The review organizes Exact Renormalization Group methods and argues, via a dual-action construction, that the anomalous dimension at critical fixed points takes only discrete values.

Show 1 more citing papers

Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
hep-th 2013-06 conditional novelty 5.0 of 10

The f(R) approximation to asymptotic safety, as formulated by Benedetti and Caravelli, degenerates on four-spheres: because the fixed point has no constant-curvature vacuum, every eigenoperator is redundant and the pe...

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