Liquid-Gas Criticality of Hyperuniform Fluids

In statistical physics, it is well established that the liquid-gas (LG) phase transition with divergent critical fluctuations belongs to the Ising universality class. Whether nonequilibrium effects can alter this universal behavior remains a fundamental open question. In this work, we theoretically prove that nonequilibrium hyperuniform (HU) fluids with additional center-of-mass conservation exhibit LG criticality different from the Ising universality class. As a specific case, we investigate a 2D HU fluid composed of active spinners, where phase separation is driven by dissipative collisions. Strikingly, at the critical point, the 2D HU fluid displays finite density fluctuations <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>S</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>q</a:mi> <a:mo stretchy="false">)</a:mo> <a:mo>∼</a:mo> <a:msup> <a:mrow> <a:mi>q</a:mi> </a:mrow> <a:mrow> <a:mi>η</a:mi> </a:mrow> </a:msup> <a:mo>∼</a:mo> <a:mi>const</a:mi> </a:mrow> </a:math> with <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>η</e:mi> <e:mo>=</e:mo> <e:mn>0</e:mn> </e:math> , rather than the expected divergence <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>S</g:mi> <g:mo stretchy="false">(</g:mo> <g:mi>q</g:mi> <g:mo stretchy="false">)</g:mo> <g:mo>∼</g:mo> <g:msup> <g:mi>q</g:mi> <g:mrow> <g:mi>η</g:mi> <g:mo>−</g:mo> <g:mn>2</g:mn> </g:mrow> </g:msup> </g:math> with <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>η</k:mi> <k:mo>=</k:mo> <k:mn>1</k:mn> <k:mo>/</k:mo> <k:mn>4</k:mn> </k:math> as in the Ising model, while the compressibility still diverges. The critical point is thus calm yet highly susceptible, in fundamental violation of the conventional fluctuation-dissipation relation. Consistently, we observe short-range pair correlation functions coexisting with quasi-long-range response functions at the critical point. Based on a generalized model <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mi>B</m:mi> </m:mrow> </m:math> and renormalization-group analysis, we prove that hyperuniformity reduces the upper critical dimension <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>d</o:mi> <o:mi>c</o:mi> </o:msub> </o:math> from 4 to 2. Moreover, the critical point exhibits Gaussian density fluctuations indicated by Binder cumulant, distinct from non-Gaussian critical behaviors of the mean-field Ising universality class. The system also exhibits nondivergent energy fluctuations rather than logarithmic divergence as expected in the Ising universality class at <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>d</q:mi> <q:mo>=</q:mo> <q:msub> <q:mi>d</q:mi> <q:mi>c</q:mi> </q:msub> </q:math> . Furthermore, the HU fluid undergoes nonconventional spinodal decomposition, where the decomposition time diverges but the characteristic length scale remains finite as the critical point is approached. The origin of the above anomalies lies in the nonequilibrium nature of the system which obeys a generalized fluctuation-dissipation relation <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mn>2</s:mn> <s:mi>Im</s:mi> <s:mi>χ</s:mi> <s:mo stretchy="false">(</s:mo> <s:mi>q</s:mi> <s:mo>,</s:mo> <s:mi>ω</s:mi> <s:mo stretchy="false">)</s:mo> <s:mo>=</s:mo> <s:mi>ω</s:mi> <s:mi>C</s:mi> <s:mo stretchy="false">(</s:mo> <s:mi>q</s:mi> <s:mo>,</s:mo> <s:mi>ω</s:mi> <s:mo stretchy="false">)</s:mo> <s:mo>/</s:mo> <s:mrow> <s:msub> <s:mi>k</s:mi> <s:mi>B</s:mi> </s:msub> <s:msub> <s:mi>T</s:mi> <s:mi>eff</s:mi> </s:msub> <s:mo stretchy="false">(</s:mo> <s:mi>q</s:mi> <s:mo stretchy="false">)</s:mo> </s:mrow> </s:math> with a scale-dependent effective temperature <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>T</ab:mi> <ab:mi>eff</ab:mi> </ab:msub> <ab:mo stretchy="false">(</ab:mo> <ab:mi>q</ab:mi> <ab:mo stretchy="false">)</ab:mo> <ab:mo>∝</ab:mo> <ab:msup> <ab:mi>q</ab:mi> <ab:mn>2</ab:mn> </ab:msup> </ab:math> . These findings establish a striking exception to conventional paradigms of critical phenomena and illustrate how nonequilibrium forces can fundamentally reshape universality classes.