article published yes Simona Colabrese author Daniele De Martino author 3FF5848A-F248-11E8-B48F-1D18A9856A870000-0002-5214-4706 Luca Leuzzi author Enzo Marinari author GaTk department International IST Postdoc Fellowship Programme project The resolution of a linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density c and the ratio α=N/M between number of variables N and number of constraints M. By means of ensemble calculations we show that the space of feasible solutions endows a Van-Der-Waals phase diagram in the plane (c, α). We give numerical evidence that the associated computational problems become more difficult across the critical point and in particular in the coexistence region. IOP Publishing2017 eng 1742-5468 1705.06303 00041184290000110.1088/1742-5468/aa85c3 20179 Colabrese S, De Martino D, Leuzzi L, Marinari E. 2017. Phase transitions in integer linear problems. Journal of Statistical Mechanics: Theory and Experiment. 2017(9), 093404. S. Colabrese, D. De Martino, L. Leuzzi, E. Marinari, Journal of Statistical Mechanics: Theory and Experiment 2017 (2017). Colabrese S, De Martino D, Leuzzi L, Marinari E. Phase transitions in integer linear problems. <i> Journal of Statistical Mechanics: Theory and Experiment</i>. 2017;2017(9). doi:<a href="https://doi.org/10.1088/1742-5468/aa85c3">10.1088/1742-5468/aa85c3</a> Colabrese, Simona, et al. “Phase Transitions in Integer Linear Problems.” <i> Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2017, no. 9, 093404, IOP Publishing, 2017, doi:<a href="https://doi.org/10.1088/1742-5468/aa85c3">10.1088/1742-5468/aa85c3</a>. S. Colabrese, D. De Martino, L. Leuzzi, and E. Marinari, “Phase transitions in integer linear problems,” <i> Journal of Statistical Mechanics: Theory and Experiment</i>, vol. 2017, no. 9. IOP Publishing, 2017. Colabrese, Simona, Daniele De Martino, Luca Leuzzi, and Enzo Marinari. “Phase Transitions in Integer Linear Problems.” <i> Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing, 2017. <a href="https://doi.org/10.1088/1742-5468/aa85c3">https://doi.org/10.1088/1742-5468/aa85c3</a>. Colabrese, S., De Martino, D., Leuzzi, L., &#38; Marinari, E. (2017). Phase transitions in integer linear problems. <i> Journal of Statistical Mechanics: Theory and Experiment</i>. IOP Publishing. <a href="https://doi.org/10.1088/1742-5468/aa85c3">https://doi.org/10.1088/1742-5468/aa85c3</a> 8232018-12-11T11:48:41Z2025-06-04T08:08:31Z