Separating Field--Camp Alignment from Structural Balance in a Frustrated Random-Field Ising Model of Social Networks
Abstract
Frustrated Ising models of social networks mix ferromagnetic (agreement-seeking) and antiferromagnetic (antagonistic) couplings, and the antagonistic bonds are almost always placed independently at a fixed rate, yielding a +/-J spin glass. Real signed networks (Epinions, Slashdot, Wikipedia) instead show an excess of balanced triads, and perfectly balanced placement is gauge-equivalent to an unfrustrated ferromagnet. We compare three sign-placement conditions on a frustrated random-field Ising model of a polarised population, sharing an identical graph, field assignment, and edge-weight magnitudes: an independent baseline; a balance-structured condition whose camp membership coincides with each voter's field sign; and the same condition with camp labels randomly permuted, so triadic balance is identical by construction while the camp-field correlation is removed. On a confound-controlled Kolmogorov-Smirnov test of the sampled energy-gap distribution (simulated annealing), the aligned condition differs from the baseline at every density tested (p = 7.3e-8), while the permuted condition shows no significant difference (paired mean difference 0.003, 95% CI [-0.041, 0.046]). Field-camp alignment, not triadic balance alone, drives the effect. The qualitative direction follows from a known mapping; the contribution is a quantitative, confound-controlled measurement of the effect's size away from that limit, robust to parallel-tempering sampling, system sizes up to N = 300, and structural noise calibrated to real networks, while triadic balance alone produces no detectable effect at N = 90 and at most a small one at N = 180-300 (paired change in KS distance about 0.04, 95% CI upper bound below 0.09).
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BibTeX
@misc{romero2026separating,
title = {{Separating Field--Camp Alignment from Structural Balance in a Frustrated Random-Field Ising Model of Social Networks}},
author = {Natalia Romero},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12578},
eprint = {2610.12578},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12578},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Separating Field--Camp Alignment from Structural Balance in a Frustrated Random-Field Ising Model of Social Networks
AU - Natalia Romero
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12578
UR - https://arxiv.org/abs/2610.12578
AB - Frustrated Ising models of social networks mix ferromagnetic (agreement-seeking) and antiferromagnetic (antagonistic) couplings, and the antagonistic bonds are almost always placed independently at a fixed rate, yielding a +/-J spin glass. Real signed networks (Epinions, Slashdot, Wikipedia) instead show an excess of balanced triads, and perfectly balanced placement is gauge-equivalent to an unfrustrated ferromagnet. We compare three sign-placement conditions on a frustrated random-field Ising model of a polarised population, sharing an identical graph, field assignment, and edge-weight magnitudes: an independent baseline; a balance-structured condition whose camp membership coincides with each voter's field sign; and the same condition with camp labels randomly permuted, so triadic balance is identical by construction while the camp-field correlation is removed. On a confound-controlled Kolmogorov-Smirnov test of the sampled energy-gap distribution (simulated annealing), the aligned condition differs from the baseline at every density tested (p = 7.3e-8), while the permuted condition shows no significant difference (paired mean difference 0.003, 95% CI [-0.041, 0.046]). Field-camp alignment, not triadic balance alone, drives the effect. The qualitative direction follows from a known mapping; the contribution is a quantitative, confound-controlled measurement of the effect's size away from that limit, robust to parallel-tempering sampling, system sizes up to N = 300, and structural noise calibrated to real networks, while triadic balance alone produces no detectable effect at N = 90 and at most a small one at N = 180-300 (paired change in KS distance about 0.04, 95% CI upper bound below 0.09).
ER -