Frustrated Ising model on the honeycomb lattice: Metastability and universality

We study the Ising model with competing ferromagnetic nearest- and antiferromagnetic next-nearest-neighbor interactions of strengths <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>J</a:mi> <a:mn>1</a:mn> </a:msub> <a:mo>&gt;</a:mo> <a:mn>0</a:mn> </a:mrow> </a:math> and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>J</b:mi> <b:mn>2</b:mn> </b:msub> <b:mo>&lt;</b:mo> <b:mn>0</b:mn> </b:mrow> </b:math> , respectively, on the honeycomb lattice. For <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>J</c:mi> <c:mn>2</c:mn> </c:msub> <c:mo>&gt;</c:mo> <c:mo>−</c:mo> <c:msub> <c:mi>J</c:mi> <c:mn>1</c:mn> </c:msub> <c:mo>/</c:mo> <c:mn>4</c:mn> </c:mrow> </c:math> it has a ferromagnetic ground state, and previous work has shown that at least for <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi>J</d:mi> <d:mn>2</d:mn> </d:msub> <d:mo>≳</d:mo> <d:mo>−</d:mo> <d:mn>0.2</d:mn> <d:msub> <d:mi>J</d:mi> <d:mn>1</d:mn> </d:msub> </d:mrow> </d:math> the transition is in the Ising universality class. For even lower <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>J</e:mi> <e:mn>2</e:mn> </e:msub> </e:math> some indicators pointing towards a first-order transition were reported. By utilizing population annealing Monte Carlo simulations together with a rejection-free and adaptive update, we can equilibrate systems with <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>J</f:mi> <f:mn>2</f:mn> </f:msub> </f:math> as low as <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mo>−</g:mo> <g:mn>0.23</g:mn> <g:msub> <g:mi>J</g:mi> <g:mn>1</g:mn> </g:msub> </g:mrow> </g:math> . By means of a finite-size scaling analysis we show that the system undergoes a second-order phase transition within the Ising universality class at least down to <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>J</h:mi> <h:mn>2</h:mn> </h:msub> <h:mo>=</h:mo> <h:mo>−</h:mo> <h:mn>0.23</h:mn> <h:msub> <h:mi>J</h:mi> <h:mn>1</h:mn> </h:msub> </h:mrow> </h:math> and, most likely, for all <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:msub> <i:mi>J</i:mi> <i:mn>2</i:mn> </i:msub> <i:mo>&gt;</i:mo> <i:mo>−</i:mo> <i:msub> <i:mi>J</i:mi> <i:mn>1</i:mn> </i:msub> <i:mo>/</i:mo> <i:mn>4</i:mn> </i:mrow> </i:math> . As we show here, there exist very long-lived metastable states in this system explaining the first-order like behavior seen in only partially equilibrated systems.