Weak first-order phase transitions in the frustrated square lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>J</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> classical Ising model
Bibliographic record
Abstract
The classical ${J}_{1}\ensuremath{-}{J}_{2}$ Ising model on the square lattice is a minimal model of frustrated magnetism whose phase boundaries have remained under scrutiny for decades. Signs of first-order phase transitions have appeared in some studies, but strong evidence remains lacking. The current consensus, based upon the numerical data and theoretical arguments in [S. Jin et al., Phys. Rev. Lett. 108, 045702 (2012)], is that first-order phase transitions are ruled out in the region $g={J}_{2}/|{J}_{1}|\ensuremath{\gtrsim}0.67$. We point out a loophole in the basis for this consensus, and we find strong evidence that the phase boundary is instead weak first order at $0.67\ensuremath{\lesssim}g<\ensuremath{\infty}$ such that it asymptotically becomes second order when $g\ensuremath{\rightarrow}\ensuremath{\infty}$. We also find strong evidence that the phase boundary is first order in the region $0.5<g\ensuremath{\lesssim}0.67$. We establish these results with adiabatic evolution of matrix product states directly in the thermodynamic limit, and with the theory of finite-entanglement scaling. We also find suggestive evidence that when $g\ensuremath{\rightarrow}0.{5}^{+}$, the phase boundary becomes of an anomalous first-order type wherein the correlation length is very large in one of the coexisting phases but very small in the other.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.001 | 0.006 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.140 | 0.008 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".