Ising-like model replicating time-averaged neural spiking The activity of the resting state of the brain exhibits avalanches of spiking activity of sizes that follow a power-law distribution. In an attempt to grasp brain criticality we investigate the spiking patterns of in vitro rat cortices and in vivo mice cortices as well as of an Integrate-and-Fire (IF) model that can be tuned at criticality. Through a Pairwise Maximum-Entropy method, we identify through an inverse binary Ising-like model the local fields and interaction couplings which best reproduce the average activities of each neuron as well as the statistical correlations between the activities of each pair of them in the system. The activity of the neurons is mainly stored in the local fields, while a symmetric distribution of interaction constants which becomes sharper with system size seems generic. Interestingly, for the in vitro rat cortex data the three–point correlations are remarkably well reproduced. Under the framework of the inherent thermodynamic analogy brought by the Ising-like models built in this work, we found through Monte Carlo simulations that they exhibit in all cases second-order phase transitions between ferromagnetic and paramagnetic phases at a temperature consistent with Tc = 1, which is exactly the temperature used in the Maximum-Entropy method. The numerical data from the IF model allow to study systematically the dependence on parameters like size and concentration of inhibitory neurons avoiding the use of subsampling. We found that networks with higher percentage of inhibitory neurons lead to Ising-like systems with reduced thermal fluctuations. Finally, considering only neuronal pairs associated with the largest correlation functions allows the study of larger system sizes.