Many physical systems, including some examples of active matter, granular assemblies, and biological systems, show fluctuation-dominated phase ordering (FDPO), where macroscopic fluctuations coexist with long-range order. Most of these systems are out of equilibrium. By contrast, a recent work has analytically demonstrated that an equilibrium one-dimensional truncated inverse distance square Ising (TIDSI) model shows FDPO. The analytical results rely on a cluster representation of the model that we term TIDSI-CL and are governed by the ratio, $c$, of the long-range interaction strength to the critical temperature. We show that the allowed range of $c$ is very narrow in the original TIDSI model while it is unbounded in TIDSI-CL. We perform Monte Carlo simulations for the TIDSI model and show consistency with the analytical results in the allowed range of $c$. The correlation length grows strongly on approaching the critical point, leading to a broad near-critical region. Within this region, $\alpha$, which is the cusp exponent of the power-law decay of the scaled correlation function at criticality, changes to ${\alpha }^{\text{eff}}$. We also investigate the coarsening dynamics of the model: The correlation function, domain size distribution, and aging behavior are consistent with the equilibrium properties upon replacing the system size, $L$, by the coarsening length, $\mathcal{L}\left(t\right)$. The mean largest cluster size shows logarithmic corrections due to finite $L$ and waiting time, $t_w$. The aging autocorrelation function exhibits two different scaling forms, characterized by exponents $\beta$ and $\gamma$, at short and long times compared to $t_w$, where $\beta =\alpha /2$.

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• Classical statistical mechanics
• Fluctuations & noise
• Long-range interactions
• Macroscopic fluctuation theory
• Phase behavior
• Classical spin models
• Ising model
• Monte Carlo methods