Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>t</mml:mi> <mml:mtext>−</mml:mtext> <mml:mi>J</mml:mi> </mml:mrow>

We study the two-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>t</a:mi> <a:mtext>−</a:mtext> <a:mi>J</a:mi> </a:mrow> </a:math> model at finite temperature directly in the thermodynamic limit using purification represented by an infinite projected entangled-pair state (iPEPS). We reach temperatures down to <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>T</b:mi> <b:mo>/</b:mo> <b:mi>t</b:mi> <b:mo>=</b:mo> <b:mn>0.1</b:mn> </b:mrow> </b:math> and hole concentrations up to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mn>1</c:mn> <c:mo>−</c:mo> <c:mi>n</c:mi> <c:mo>≃</c:mo> <c:mn>0.25</c:mn> </c:mrow> </c:math> , and provide benchmark thermodynamic-limit results for the specific heat, uniform susceptibility, and charge compressibility. We identify a susceptibility maximum <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msup> <d:mi>T</d:mi> <d:mo>*</d:mo> </d:msup> </d:math> that tracks the buildup of short-range antiferromagnetism and a shallow compressibility enhancement upon cooling in the same doping window. To expose the underlying microscopic mechanism, we introduce dopant-conditioned multipoint correlators that quantify how holes reorganize nearby exchange: Single holes weaken adjacent antiferromagnetic bonds, while nearest-neighbor hole pairs produce a cooperative response that reinforces antiferromagnetism on the parallel plaquette edge. Over the same parameter window, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>d</e:mi> </e:math> -wave pairing correlations remain short-ranged. These results provide experiment-compatible thermodynamic-limit benchmarks and establish dopant-conditioned correlators as incisive probes of finite-temperature spin-texture reorganization in doped Mott insulators.