Unraveling the challenges of phase transition and temperature-dependent thermal conductivity in the one-dimensional rotor model

The one-dimensional rotor model is a classical momentum-conserving system that exhibits normal heat conduction, making it a valuable platform for studying thermal transport. Despite progress in understanding its transport properties, two key issues remain open: (1) whether a phase transition from normal to anomalous heat conduction occurs as temperature decreases and (2) how thermal conductivity <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>κ</a:mi></a:math> depends on temperature. Using molecular dynamics simulations and Green-Kubo formalism, we demonstrate that although normal conduction may persist theoretically at any nonzero temperature, the exponentially increasing mean free path at low temperatures renders it practically unobservable, supporting the existence of an effective phase transition. Furthermore, we find that <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>κ</b:mi></b:math> exhibits a double-exponential temperature dependence—<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>κ</c:mi><c:mo>∼</c:mo><c:msup><c:mi>e</c:mi><c:mrow><c:mrow><c:mn>2.54</c:mn></c:mrow><c:mi>T</c:mi></c:mrow></c:msup></c:mrow></c:math> at high temperatures and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>κ</d:mi><d:mo>∼</d:mo><d:msup><d:mi>e</d:mi><d:mrow><d:mrow><d:mn>0.49</d:mn></d:mrow><d:mi>T</d:mi></d:mrow></d:msup></d:mrow></d:math> at low temperatures—with an intermediate power-law regime <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>κ</e:mi><e:mo>∼</e:mo><e:msup><e:mi>T</e:mi><e:mrow><e:mo>−</e:mo><e:mn>3.2</e:mn></e:mrow></e:msup></e:mrow></e:math> dominated by nonlinearity. To isolate the role of nonlinearity, we study a modified rotor model with suppressed phase jumps, which exhibits <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>κ</f:mi><f:mo>∼</f:mo><f:msup><f:mi>T</f:mi><f:mrow><f:mo>−</f:mo><f:mn>3.6</f:mn></f:mrow></f:msup></f:mrow></f:math>, confirming the influence of interaction nonlinearity. These findings deepen the understanding of temperature-dependent transport in low-dimensional systems.